YES Problem: active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(plus(x(N,M),N)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) Proof: DP Processor: DPs: active#(and(tt(),X)) -> mark#(X) active#(plus(N,0())) -> mark#(N) active#(plus(N,s(M))) -> plus#(N,M) active#(plus(N,s(M))) -> s#(plus(N,M)) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) active#(x(N,0())) -> mark#(0()) active#(x(N,s(M))) -> x#(N,M) active#(x(N,s(M))) -> plus#(x(N,M),N) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> and#(mark(X1),X2) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(tt()) -> active#(tt()) mark#(plus(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(0()) -> active#(0()) mark#(s(X)) -> mark#(X) mark#(s(X)) -> s#(mark(X)) mark#(s(X)) -> active#(s(mark(X))) mark#(x(X1,X2)) -> mark#(X2) mark#(x(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> x#(mark(X1),mark(X2)) mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) and#(mark(X1),X2) -> and#(X1,X2) and#(X1,mark(X2)) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) plus#(mark(X1),X2) -> plus#(X1,X2) plus#(X1,mark(X2)) -> plus#(X1,X2) plus#(active(X1),X2) -> plus#(X1,X2) plus#(X1,active(X2)) -> plus#(X1,X2) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) x#(mark(X1),X2) -> x#(X1,X2) x#(X1,mark(X2)) -> x#(X1,X2) x#(active(X1),X2) -> x#(X1,X2) x#(X1,active(X2)) -> x#(X1,X2) TRS: active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(plus(x(N,M),N)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) TDG Processor: DPs: active#(and(tt(),X)) -> mark#(X) active#(plus(N,0())) -> mark#(N) active#(plus(N,s(M))) -> plus#(N,M) active#(plus(N,s(M))) -> s#(plus(N,M)) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) active#(x(N,0())) -> mark#(0()) active#(x(N,s(M))) -> x#(N,M) active#(x(N,s(M))) -> plus#(x(N,M),N) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> and#(mark(X1),X2) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(tt()) -> active#(tt()) mark#(plus(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(0()) -> active#(0()) mark#(s(X)) -> mark#(X) mark#(s(X)) -> s#(mark(X)) mark#(s(X)) -> active#(s(mark(X))) mark#(x(X1,X2)) -> mark#(X2) mark#(x(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> x#(mark(X1),mark(X2)) mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) and#(mark(X1),X2) -> and#(X1,X2) and#(X1,mark(X2)) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) plus#(mark(X1),X2) -> plus#(X1,X2) plus#(X1,mark(X2)) -> plus#(X1,X2) plus#(active(X1),X2) -> plus#(X1,X2) plus#(X1,active(X2)) -> plus#(X1,X2) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) x#(mark(X1),X2) -> x#(X1,X2) x#(X1,mark(X2)) -> x#(X1,X2) x#(active(X1),X2) -> x#(X1,X2) x#(X1,active(X2)) -> x#(X1,X2) TRS: active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(plus(x(N,M),N)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) graph: and#(mark(X1),X2) -> and#(X1,X2) -> and#(X1,active(X2)) -> and#(X1,X2) and#(mark(X1),X2) -> and#(X1,X2) -> and#(active(X1),X2) -> and#(X1,X2) and#(mark(X1),X2) -> and#(X1,X2) -> and#(X1,mark(X2)) -> and#(X1,X2) and#(mark(X1),X2) -> and#(X1,X2) -> and#(mark(X1),X2) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) -> and#(X1,active(X2)) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) -> and#(active(X1),X2) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) -> and#(X1,mark(X2)) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) -> and#(mark(X1),X2) -> and#(X1,X2) and#(X1,mark(X2)) -> and#(X1,X2) -> and#(X1,active(X2)) -> and#(X1,X2) and#(X1,mark(X2)) -> and#(X1,X2) -> and#(active(X1),X2) -> and#(X1,X2) and#(X1,mark(X2)) -> and#(X1,X2) -> and#(X1,mark(X2)) -> and#(X1,X2) and#(X1,mark(X2)) -> and#(X1,X2) -> and#(mark(X1),X2) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) -> and#(X1,active(X2)) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) -> and#(active(X1),X2) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) -> and#(X1,mark(X2)) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) -> and#(mark(X1),X2) -> and#(X1,X2) x#(mark(X1),X2) -> x#(X1,X2) -> x#(X1,active(X2)) -> x#(X1,X2) x#(mark(X1),X2) -> x#(X1,X2) -> x#(active(X1),X2) -> x#(X1,X2) x#(mark(X1),X2) -> x#(X1,X2) -> x#(X1,mark(X2)) -> x#(X1,X2) x#(mark(X1),X2) -> x#(X1,X2) -> x#(mark(X1),X2) -> x#(X1,X2) x#(active(X1),X2) -> x#(X1,X2) -> x#(X1,active(X2)) -> x#(X1,X2) x#(active(X1),X2) -> x#(X1,X2) -> x#(active(X1),X2) -> x#(X1,X2) x#(active(X1),X2) -> x#(X1,X2) -> x#(X1,mark(X2)) -> x#(X1,X2) x#(active(X1),X2) -> x#(X1,X2) -> x#(mark(X1),X2) -> x#(X1,X2) x#(X1,mark(X2)) -> x#(X1,X2) -> x#(X1,active(X2)) -> x#(X1,X2) x#(X1,mark(X2)) -> x#(X1,X2) -> x#(active(X1),X2) -> x#(X1,X2) x#(X1,mark(X2)) -> x#(X1,X2) -> x#(X1,mark(X2)) -> x#(X1,X2) x#(X1,mark(X2)) -> x#(X1,X2) -> x#(mark(X1),X2) -> x#(X1,X2) x#(X1,active(X2)) -> x#(X1,X2) -> x#(X1,active(X2)) -> x#(X1,X2) x#(X1,active(X2)) -> x#(X1,X2) -> x#(active(X1),X2) -> x#(X1,X2) x#(X1,active(X2)) -> x#(X1,X2) -> x#(X1,mark(X2)) -> x#(X1,X2) x#(X1,active(X2)) -> x#(X1,X2) -> x#(mark(X1),X2) -> x#(X1,X2) s#(mark(X)) -> s#(X) -> s#(active(X)) -> s#(X) s#(mark(X)) -> s#(X) -> s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) -> s#(active(X)) -> s#(X) s#(active(X)) -> s#(X) -> s#(mark(X)) -> s#(X) plus#(mark(X1),X2) -> plus#(X1,X2) -> plus#(X1,active(X2)) -> plus#(X1,X2) plus#(mark(X1),X2) -> plus#(X1,X2) -> plus#(active(X1),X2) -> plus#(X1,X2) plus#(mark(X1),X2) -> plus#(X1,X2) -> plus#(X1,mark(X2)) -> plus#(X1,X2) plus#(mark(X1),X2) -> plus#(X1,X2) -> plus#(mark(X1),X2) -> plus#(X1,X2) plus#(active(X1),X2) -> plus#(X1,X2) -> plus#(X1,active(X2)) -> plus#(X1,X2) plus#(active(X1),X2) -> plus#(X1,X2) -> plus#(active(X1),X2) -> plus#(X1,X2) plus#(active(X1),X2) -> plus#(X1,X2) -> plus#(X1,mark(X2)) -> plus#(X1,X2) plus#(active(X1),X2) -> plus#(X1,X2) -> plus#(mark(X1),X2) -> plus#(X1,X2) plus#(X1,mark(X2)) -> plus#(X1,X2) -> plus#(X1,active(X2)) -> plus#(X1,X2) plus#(X1,mark(X2)) -> plus#(X1,X2) -> plus#(active(X1),X2) -> plus#(X1,X2) plus#(X1,mark(X2)) -> plus#(X1,X2) -> plus#(X1,mark(X2)) -> plus#(X1,X2) plus#(X1,mark(X2)) -> plus#(X1,X2) -> plus#(mark(X1),X2) -> plus#(X1,X2) plus#(X1,active(X2)) -> plus#(X1,X2) -> plus#(X1,active(X2)) -> plus#(X1,X2) plus#(X1,active(X2)) -> plus#(X1,X2) -> plus#(active(X1),X2) -> plus#(X1,X2) plus#(X1,active(X2)) -> plus#(X1,X2) -> plus#(X1,mark(X2)) -> plus#(X1,X2) plus#(X1,active(X2)) -> plus#(X1,X2) -> plus#(mark(X1),X2) -> plus#(X1,X2) mark#(x(X1,X2)) -> x#(mark(X1),mark(X2)) -> x#(X1,active(X2)) -> x#(X1,X2) mark#(x(X1,X2)) -> x#(mark(X1),mark(X2)) -> x#(active(X1),X2) -> x#(X1,X2) mark#(x(X1,X2)) -> x#(mark(X1),mark(X2)) -> x#(X1,mark(X2)) -> x#(X1,X2) mark#(x(X1,X2)) -> x#(mark(X1),mark(X2)) -> x#(mark(X1),X2) -> x#(X1,X2) mark#(x(X1,X2)) -> mark#(X2) -> mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) mark#(x(X1,X2)) -> mark#(X2) -> mark#(x(X1,X2)) -> x#(mark(X1),mark(X2)) mark#(x(X1,X2)) -> mark#(X2) -> mark#(x(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X2) -> mark#(x(X1,X2)) -> mark#(X2) mark#(x(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> active#(s(mark(X))) mark#(x(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> s#(mark(X)) mark#(x(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X) mark#(x(X1,X2)) -> mark#(X2) -> mark#(0()) -> active#(0()) mark#(x(X1,X2)) -> mark#(X2) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(x(X1,X2)) -> mark#(X2) -> mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) mark#(x(X1,X2)) -> mark#(X2) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X2) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(x(X1,X2)) -> mark#(X2) -> mark#(tt()) -> active#(tt()) mark#(x(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(x(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) mark#(x(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) mark#(x(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> x#(mark(X1),mark(X2)) mark#(x(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X2) mark#(x(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> active#(s(mark(X))) mark#(x(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> s#(mark(X)) mark#(x(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(x(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(x(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(x(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) mark#(x(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(x(X1,X2)) -> mark#(X1) -> mark#(tt()) -> active#(tt()) mark#(x(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(x(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) mark#(x(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) -> active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) -> active#(x(N,s(M))) -> plus#(x(N,M),N) mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) -> active#(x(N,s(M))) -> x#(N,M) mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) -> active#(x(N,0())) -> mark#(0()) mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) -> active#(plus(N,s(M))) -> mark#(s(plus(N,M))) mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) -> active#(plus(N,s(M))) -> s#(plus(N,M)) mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) -> active#(plus(N,s(M))) -> plus#(N,M) mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) -> active#(plus(N,0())) -> mark#(N) mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) -> active#(and(tt(),X)) -> mark#(X) mark#(s(X)) -> s#(mark(X)) -> s#(active(X)) -> s#(X) mark#(s(X)) -> s#(mark(X)) -> s#(mark(X)) -> s#(X) mark#(s(X)) -> mark#(X) -> mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) mark#(s(X)) -> mark#(X) -> mark#(x(X1,X2)) -> x#(mark(X1),mark(X2)) mark#(s(X)) -> mark#(X) -> mark#(x(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(x(X1,X2)) -> mark#(X2) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(mark(X))) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> s#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(s(X)) -> mark#(X) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(s(X)) -> mark#(X) -> mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) mark#(s(X)) -> mark#(X) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(s(X)) -> mark#(X) -> mark#(tt()) -> active#(tt()) mark#(s(X)) -> mark#(X) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(s(X)) -> mark#(X) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) mark#(s(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) mark#(s(X)) -> active#(s(mark(X))) -> active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) mark#(s(X)) -> active#(s(mark(X))) -> active#(x(N,s(M))) -> plus#(x(N,M),N) mark#(s(X)) -> active#(s(mark(X))) -> active#(x(N,s(M))) -> x#(N,M) mark#(s(X)) -> active#(s(mark(X))) -> active#(x(N,0())) -> mark#(0()) mark#(s(X)) -> active#(s(mark(X))) -> active#(plus(N,s(M))) -> mark#(s(plus(N,M))) mark#(s(X)) -> active#(s(mark(X))) -> active#(plus(N,s(M))) -> s#(plus(N,M)) mark#(s(X)) -> active#(s(mark(X))) -> active#(plus(N,s(M))) -> plus#(N,M) mark#(s(X)) -> active#(s(mark(X))) -> active#(plus(N,0())) -> mark#(N) mark#(s(X)) -> active#(s(mark(X))) -> active#(and(tt(),X)) -> mark#(X) mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) -> plus#(X1,active(X2)) -> plus#(X1,X2) mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) -> plus#(active(X1),X2) -> plus#(X1,X2) mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) -> plus#(X1,mark(X2)) -> plus#(X1,X2) mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) -> plus#(mark(X1),X2) -> plus#(X1,X2) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(x(X1,X2)) -> x#(mark(X1),mark(X2)) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(x(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(x(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> active#(s(mark(X))) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> s#(mark(X)) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(0()) -> active#(0()) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(tt()) -> active#(tt()) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> x#(mark(X1),mark(X2)) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> active#(s(mark(X))) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> s#(mark(X)) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(tt()) -> active#(tt()) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(x(N,s(M))) -> plus#(x(N,M),N) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(x(N,s(M))) -> x#(N,M) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(x(N,0())) -> mark#(0()) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(plus(N,s(M))) -> mark#(s(plus(N,M))) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(plus(N,s(M))) -> s#(plus(N,M)) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(plus(N,s(M))) -> plus#(N,M) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(plus(N,0())) -> mark#(N) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(and(tt(),X)) -> mark#(X) mark#(0()) -> active#(0()) -> active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) mark#(0()) -> active#(0()) -> active#(x(N,s(M))) -> plus#(x(N,M),N) mark#(0()) -> active#(0()) -> active#(x(N,s(M))) -> x#(N,M) mark#(0()) -> active#(0()) -> active#(x(N,0())) -> mark#(0()) mark#(0()) -> active#(0()) -> active#(plus(N,s(M))) -> mark#(s(plus(N,M))) mark#(0()) -> active#(0()) -> active#(plus(N,s(M))) -> s#(plus(N,M)) mark#(0()) -> active#(0()) -> active#(plus(N,s(M))) -> plus#(N,M) mark#(0()) -> active#(0()) -> active#(plus(N,0())) -> mark#(N) mark#(0()) -> active#(0()) -> active#(and(tt(),X)) -> mark#(X) mark#(and(X1,X2)) -> and#(mark(X1),X2) -> and#(X1,active(X2)) -> and#(X1,X2) mark#(and(X1,X2)) -> and#(mark(X1),X2) -> and#(active(X1),X2) -> and#(X1,X2) mark#(and(X1,X2)) -> and#(mark(X1),X2) -> and#(X1,mark(X2)) -> and#(X1,X2) mark#(and(X1,X2)) -> and#(mark(X1),X2) -> and#(mark(X1),X2) -> and#(X1,X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) mark#(and(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> x#(mark(X1),mark(X2)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> active#(s(mark(X))) mark#(and(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> s#(mark(X)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(and(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(and(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(tt()) -> active#(tt()) mark#(and(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(x(N,s(M))) -> plus#(x(N,M),N) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(x(N,s(M))) -> x#(N,M) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(x(N,0())) -> mark#(0()) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(plus(N,s(M))) -> mark#(s(plus(N,M))) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(plus(N,s(M))) -> s#(plus(N,M)) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(plus(N,s(M))) -> plus#(N,M) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(plus(N,0())) -> mark#(N) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(and(tt(),X)) -> mark#(X) mark#(tt()) -> active#(tt()) -> active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) mark#(tt()) -> active#(tt()) -> active#(x(N,s(M))) -> plus#(x(N,M),N) mark#(tt()) -> active#(tt()) -> active#(x(N,s(M))) -> x#(N,M) mark#(tt()) -> active#(tt()) -> active#(x(N,0())) -> mark#(0()) mark#(tt()) -> active#(tt()) -> active#(plus(N,s(M))) -> mark#(s(plus(N,M))) mark#(tt()) -> active#(tt()) -> active#(plus(N,s(M))) -> s#(plus(N,M)) mark#(tt()) -> active#(tt()) -> active#(plus(N,s(M))) -> plus#(N,M) mark#(tt()) -> active#(tt()) -> active#(plus(N,0())) -> mark#(N) mark#(tt()) -> active#(tt()) -> active#(and(tt(),X)) -> mark#(X) active#(x(N,s(M))) -> x#(N,M) -> x#(X1,active(X2)) -> x#(X1,X2) active#(x(N,s(M))) -> x#(N,M) -> x#(active(X1),X2) -> x#(X1,X2) active#(x(N,s(M))) -> x#(N,M) -> x#(X1,mark(X2)) -> x#(X1,X2) active#(x(N,s(M))) -> x#(N,M) -> x#(mark(X1),X2) -> x#(X1,X2) active#(x(N,s(M))) -> plus#(x(N,M),N) -> plus#(X1,active(X2)) -> plus#(X1,X2) active#(x(N,s(M))) -> plus#(x(N,M),N) -> plus#(active(X1),X2) -> plus#(X1,X2) active#(x(N,s(M))) -> plus#(x(N,M),N) -> plus#(X1,mark(X2)) -> plus#(X1,X2) active#(x(N,s(M))) -> plus#(x(N,M),N) -> plus#(mark(X1),X2) -> plus#(X1,X2) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) -> mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) -> mark#(x(X1,X2)) -> x#(mark(X1),mark(X2)) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) -> mark#(x(X1,X2)) -> mark#(X1) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) -> mark#(x(X1,X2)) -> mark#(X2) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) -> mark#(s(X)) -> active#(s(mark(X))) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) -> mark#(s(X)) -> s#(mark(X)) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) -> mark#(s(X)) -> mark#(X) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) -> mark#(0()) -> active#(0()) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) -> mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) -> mark#(plus(X1,X2)) -> mark#(X1) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) -> mark#(plus(X1,X2)) -> mark#(X2) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) -> mark#(tt()) -> active#(tt()) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) -> mark#(and(X1,X2)) -> mark#(X1) active#(x(N,0())) -> mark#(0()) -> mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) active#(x(N,0())) -> mark#(0()) -> mark#(x(X1,X2)) -> x#(mark(X1),mark(X2)) active#(x(N,0())) -> mark#(0()) -> mark#(x(X1,X2)) -> mark#(X1) active#(x(N,0())) -> mark#(0()) -> mark#(x(X1,X2)) -> mark#(X2) active#(x(N,0())) -> mark#(0()) -> mark#(s(X)) -> active#(s(mark(X))) active#(x(N,0())) -> mark#(0()) -> mark#(s(X)) -> s#(mark(X)) active#(x(N,0())) -> mark#(0()) -> mark#(s(X)) -> mark#(X) active#(x(N,0())) -> mark#(0()) -> mark#(0()) -> active#(0()) active#(x(N,0())) -> mark#(0()) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(x(N,0())) -> mark#(0()) -> mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) active#(x(N,0())) -> mark#(0()) -> mark#(plus(X1,X2)) -> mark#(X1) active#(x(N,0())) -> mark#(0()) -> mark#(plus(X1,X2)) -> mark#(X2) active#(x(N,0())) -> mark#(0()) -> mark#(tt()) -> active#(tt()) active#(x(N,0())) -> mark#(0()) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(x(N,0())) -> mark#(0()) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) active#(x(N,0())) -> mark#(0()) -> mark#(and(X1,X2)) -> mark#(X1) active#(plus(N,s(M))) -> s#(plus(N,M)) -> s#(active(X)) -> s#(X) active#(plus(N,s(M))) -> s#(plus(N,M)) -> s#(mark(X)) -> s#(X) active#(plus(N,s(M))) -> plus#(N,M) -> plus#(X1,active(X2)) -> plus#(X1,X2) active#(plus(N,s(M))) -> plus#(N,M) -> plus#(active(X1),X2) -> plus#(X1,X2) active#(plus(N,s(M))) -> plus#(N,M) -> plus#(X1,mark(X2)) -> plus#(X1,X2) active#(plus(N,s(M))) -> plus#(N,M) -> plus#(mark(X1),X2) -> plus#(X1,X2) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) -> mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) -> mark#(x(X1,X2)) -> x#(mark(X1),mark(X2)) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) -> mark#(x(X1,X2)) -> mark#(X1) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) -> mark#(x(X1,X2)) -> mark#(X2) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) -> mark#(s(X)) -> active#(s(mark(X))) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) -> mark#(s(X)) -> s#(mark(X)) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) -> mark#(s(X)) -> mark#(X) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) -> mark#(0()) -> active#(0()) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) -> mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) -> mark#(plus(X1,X2)) -> mark#(X1) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) -> mark#(plus(X1,X2)) -> mark#(X2) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) -> mark#(tt()) -> active#(tt()) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) -> mark#(and(X1,X2)) -> mark#(X1) active#(plus(N,0())) -> mark#(N) -> mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) active#(plus(N,0())) -> mark#(N) -> mark#(x(X1,X2)) -> x#(mark(X1),mark(X2)) active#(plus(N,0())) -> mark#(N) -> mark#(x(X1,X2)) -> mark#(X1) active#(plus(N,0())) -> mark#(N) -> mark#(x(X1,X2)) -> mark#(X2) active#(plus(N,0())) -> mark#(N) -> mark#(s(X)) -> active#(s(mark(X))) active#(plus(N,0())) -> mark#(N) -> mark#(s(X)) -> s#(mark(X)) active#(plus(N,0())) -> mark#(N) -> mark#(s(X)) -> mark#(X) active#(plus(N,0())) -> mark#(N) -> mark#(0()) -> active#(0()) active#(plus(N,0())) -> mark#(N) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(plus(N,0())) -> mark#(N) -> mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) active#(plus(N,0())) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X1) active#(plus(N,0())) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X2) active#(plus(N,0())) -> mark#(N) -> mark#(tt()) -> active#(tt()) active#(plus(N,0())) -> mark#(N) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(plus(N,0())) -> mark#(N) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) active#(plus(N,0())) -> mark#(N) -> mark#(and(X1,X2)) -> mark#(X1) active#(and(tt(),X)) -> mark#(X) -> mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) active#(and(tt(),X)) -> mark#(X) -> mark#(x(X1,X2)) -> x#(mark(X1),mark(X2)) active#(and(tt(),X)) -> mark#(X) -> mark#(x(X1,X2)) -> mark#(X1) active#(and(tt(),X)) -> mark#(X) -> mark#(x(X1,X2)) -> mark#(X2) active#(and(tt(),X)) -> mark#(X) -> mark#(s(X)) -> active#(s(mark(X))) active#(and(tt(),X)) -> mark#(X) -> mark#(s(X)) -> s#(mark(X)) active#(and(tt(),X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) active#(and(tt(),X)) -> mark#(X) -> mark#(0()) -> active#(0()) active#(and(tt(),X)) -> mark#(X) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(and(tt(),X)) -> mark#(X) -> mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) active#(and(tt(),X)) -> mark#(X) -> mark#(plus(X1,X2)) -> mark#(X1) active#(and(tt(),X)) -> mark#(X) -> mark#(plus(X1,X2)) -> mark#(X2) active#(and(tt(),X)) -> mark#(X) -> mark#(tt()) -> active#(tt()) active#(and(tt(),X)) -> mark#(X) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(and(tt(),X)) -> mark#(X) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) active#(and(tt(),X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) SCC Processor: #sccs: 5 #rules: 31 #arcs: 310/1521 DPs: mark#(x(X1,X2)) -> mark#(X2) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(and(tt(),X)) -> mark#(X) mark#(tt()) -> active#(tt()) active#(plus(N,0())) -> mark#(N) mark#(plus(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) mark#(0()) -> active#(0()) active#(x(N,0())) -> mark#(0()) mark#(s(X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) mark#(x(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) TRS: active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(plus(x(N,M),N)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) EDG Processor: DPs: mark#(x(X1,X2)) -> mark#(X2) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(and(tt(),X)) -> mark#(X) mark#(tt()) -> active#(tt()) active#(plus(N,0())) -> mark#(N) mark#(plus(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) mark#(0()) -> active#(0()) active#(x(N,0())) -> mark#(0()) mark#(s(X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) mark#(x(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) TRS: active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(plus(x(N,M),N)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) graph: mark#(x(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(x(X1,X2)) -> mark#(X2) -> mark#(tt()) -> active#(tt()) mark#(x(X1,X2)) -> mark#(X2) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(x(X1,X2)) -> mark#(X2) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X2) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(x(X1,X2)) -> mark#(X2) -> mark#(0()) -> active#(0()) mark#(x(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X) mark#(x(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> active#(s(mark(X))) mark#(x(X1,X2)) -> mark#(X2) -> mark#(x(X1,X2)) -> mark#(X2) mark#(x(X1,X2)) -> mark#(X2) -> mark#(x(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X2) -> mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) mark#(x(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(x(X1,X2)) -> mark#(X1) -> mark#(tt()) -> active#(tt()) mark#(x(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(x(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(x(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(x(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(x(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> active#(s(mark(X))) mark#(x(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X2) mark#(x(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) -> active#(and(tt(),X)) -> mark#(X) mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) -> active#(plus(N,0())) -> mark#(N) mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) -> active#(plus(N,s(M))) -> mark#(s(plus(N,M))) mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) -> active#(x(N,0())) -> mark#(0()) mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) -> active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) mark#(s(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(s(X)) -> mark#(X) -> mark#(tt()) -> active#(tt()) mark#(s(X)) -> mark#(X) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(s(X)) -> mark#(X) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(s(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(mark(X))) mark#(s(X)) -> mark#(X) -> mark#(x(X1,X2)) -> mark#(X2) mark#(s(X)) -> mark#(X) -> mark#(x(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) mark#(s(X)) -> active#(s(mark(X))) -> active#(and(tt(),X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) -> active#(plus(N,0())) -> mark#(N) mark#(s(X)) -> active#(s(mark(X))) -> active#(plus(N,s(M))) -> mark#(s(plus(N,M))) mark#(s(X)) -> active#(s(mark(X))) -> active#(x(N,0())) -> mark#(0()) mark#(s(X)) -> active#(s(mark(X))) -> active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(tt()) -> active#(tt()) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(0()) -> active#(0()) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> active#(s(mark(X))) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(x(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(x(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(tt()) -> active#(tt()) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> active#(s(mark(X))) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(and(tt(),X)) -> mark#(X) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(plus(N,0())) -> mark#(N) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(plus(N,s(M))) -> mark#(s(plus(N,M))) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(x(N,0())) -> mark#(0()) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(tt()) -> active#(tt()) mark#(and(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(and(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(and(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> active#(s(mark(X))) mark#(and(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(and(tt(),X)) -> mark#(X) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(plus(N,0())) -> mark#(N) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(plus(N,s(M))) -> mark#(s(plus(N,M))) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(x(N,0())) -> mark#(0()) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) -> mark#(and(X1,X2)) -> mark#(X1) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) -> mark#(plus(X1,X2)) -> mark#(X2) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) -> mark#(plus(X1,X2)) -> mark#(X1) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) -> mark#(s(X)) -> mark#(X) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) -> mark#(s(X)) -> active#(s(mark(X))) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) -> mark#(x(X1,X2)) -> mark#(X2) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) -> mark#(x(X1,X2)) -> mark#(X1) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) -> mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) active#(x(N,0())) -> mark#(0()) -> mark#(0()) -> active#(0()) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) -> mark#(and(X1,X2)) -> mark#(X1) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) -> mark#(plus(X1,X2)) -> mark#(X2) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) -> mark#(plus(X1,X2)) -> mark#(X1) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) -> mark#(s(X)) -> mark#(X) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) -> mark#(s(X)) -> active#(s(mark(X))) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) -> mark#(x(X1,X2)) -> mark#(X2) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) -> mark#(x(X1,X2)) -> mark#(X1) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) -> mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) active#(plus(N,0())) -> mark#(N) -> mark#(and(X1,X2)) -> mark#(X1) active#(plus(N,0())) -> mark#(N) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(plus(N,0())) -> mark#(N) -> mark#(tt()) -> active#(tt()) active#(plus(N,0())) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X2) active#(plus(N,0())) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X1) active#(plus(N,0())) -> mark#(N) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(plus(N,0())) -> mark#(N) -> mark#(0()) -> active#(0()) active#(plus(N,0())) -> mark#(N) -> mark#(s(X)) -> mark#(X) active#(plus(N,0())) -> mark#(N) -> mark#(s(X)) -> active#(s(mark(X))) active#(plus(N,0())) -> mark#(N) -> mark#(x(X1,X2)) -> mark#(X2) active#(plus(N,0())) -> mark#(N) -> mark#(x(X1,X2)) -> mark#(X1) active#(plus(N,0())) -> mark#(N) -> mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) active#(and(tt(),X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) active#(and(tt(),X)) -> mark#(X) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(and(tt(),X)) -> mark#(X) -> mark#(tt()) -> active#(tt()) active#(and(tt(),X)) -> mark#(X) -> mark#(plus(X1,X2)) -> mark#(X2) active#(and(tt(),X)) -> mark#(X) -> mark#(plus(X1,X2)) -> mark#(X1) active#(and(tt(),X)) -> mark#(X) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(and(tt(),X)) -> mark#(X) -> mark#(0()) -> active#(0()) active#(and(tt(),X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) active#(and(tt(),X)) -> mark#(X) -> mark#(s(X)) -> active#(s(mark(X))) active#(and(tt(),X)) -> mark#(X) -> mark#(x(X1,X2)) -> mark#(X2) active#(and(tt(),X)) -> mark#(X) -> mark#(x(X1,X2)) -> mark#(X1) active#(and(tt(),X)) -> mark#(X) -> mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) CDG Processor: DPs: mark#(x(X1,X2)) -> mark#(X2) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(and(tt(),X)) -> mark#(X) mark#(tt()) -> active#(tt()) active#(plus(N,0())) -> mark#(N) mark#(plus(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) mark#(0()) -> active#(0()) active#(x(N,0())) -> mark#(0()) mark#(s(X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) mark#(x(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) TRS: active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(plus(x(N,M),N)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) graph: mark#(x(X1,X2)) -> mark#(X2) -> mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) mark#(x(X1,X2)) -> mark#(X2) -> mark#(x(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X2) -> mark#(x(X1,X2)) -> mark#(X2) mark#(x(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> active#(s(mark(X))) mark#(x(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X) mark#(x(X1,X2)) -> mark#(X2) -> mark#(0()) -> active#(0()) mark#(x(X1,X2)) -> mark#(X2) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(x(X1,X2)) -> mark#(X2) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X2) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(x(X1,X2)) -> mark#(X2) -> mark#(tt()) -> active#(tt()) mark#(x(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(x(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) mark#(x(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X2) mark#(x(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> active#(s(mark(X))) mark#(x(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(x(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(x(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(x(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(x(X1,X2)) -> mark#(X1) -> mark#(tt()) -> active#(tt()) mark#(x(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(x(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) -> active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) -> active#(x(N,0())) -> mark#(0()) mark#(s(X)) -> mark#(X) -> mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) mark#(s(X)) -> mark#(X) -> mark#(x(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(x(X1,X2)) -> mark#(X2) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(mark(X))) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(s(X)) -> mark#(X) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(s(X)) -> mark#(X) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(s(X)) -> mark#(X) -> mark#(tt()) -> active#(tt()) mark#(s(X)) -> mark#(X) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(s(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(x(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(x(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> active#(s(mark(X))) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(0()) -> active#(0()) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(tt()) -> active#(tt()) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> active#(s(mark(X))) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(tt()) -> active#(tt()) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(plus(N,s(M))) -> mark#(s(plus(N,M))) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(plus(N,0())) -> mark#(N) mark#(and(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) mark#(and(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> active#(s(mark(X))) mark#(and(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(and(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(and(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(tt()) -> active#(tt()) mark#(and(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(and(tt(),X)) -> mark#(X) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) -> mark#(plus(X1,X2)) -> mark#(X1) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) -> mark#(plus(X1,X2)) -> mark#(X2) active#(x(N,0())) -> mark#(0()) -> mark#(0()) -> active#(0()) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) -> mark#(s(X)) -> active#(s(mark(X))) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) -> mark#(s(X)) -> mark#(X) active#(plus(N,0())) -> mark#(N) -> mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) active#(plus(N,0())) -> mark#(N) -> mark#(x(X1,X2)) -> mark#(X1) active#(plus(N,0())) -> mark#(N) -> mark#(x(X1,X2)) -> mark#(X2) active#(plus(N,0())) -> mark#(N) -> mark#(s(X)) -> active#(s(mark(X))) active#(plus(N,0())) -> mark#(N) -> mark#(s(X)) -> mark#(X) active#(plus(N,0())) -> mark#(N) -> mark#(0()) -> active#(0()) active#(plus(N,0())) -> mark#(N) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(plus(N,0())) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X1) active#(plus(N,0())) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X2) active#(plus(N,0())) -> mark#(N) -> mark#(tt()) -> active#(tt()) active#(plus(N,0())) -> mark#(N) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(plus(N,0())) -> mark#(N) -> mark#(and(X1,X2)) -> mark#(X1) active#(and(tt(),X)) -> mark#(X) -> mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) active#(and(tt(),X)) -> mark#(X) -> mark#(x(X1,X2)) -> mark#(X1) active#(and(tt(),X)) -> mark#(X) -> mark#(x(X1,X2)) -> mark#(X2) active#(and(tt(),X)) -> mark#(X) -> mark#(s(X)) -> active#(s(mark(X))) active#(and(tt(),X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) active#(and(tt(),X)) -> mark#(X) -> mark#(0()) -> active#(0()) active#(and(tt(),X)) -> mark#(X) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(and(tt(),X)) -> mark#(X) -> mark#(plus(X1,X2)) -> mark#(X1) active#(and(tt(),X)) -> mark#(X) -> mark#(plus(X1,X2)) -> mark#(X2) active#(and(tt(),X)) -> mark#(X) -> mark#(tt()) -> active#(tt()) active#(and(tt(),X)) -> mark#(X) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(and(tt(),X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) SCC Processor: #sccs: 1 #rules: 13 #arcs: 107/289 DPs: mark#(x(X1,X2)) -> mark#(X2) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(and(tt(),X)) -> mark#(X) mark#(plus(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(plus(N,0())) -> mark#(N) mark#(s(X)) -> mark#(X) mark#(x(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) TRS: active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(plus(x(N,M),N)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) Arctic Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0 + 0, [active#](x0) = x0 + 0, [x](x0, x1) = 2x0 + x1, [s](x0) = x0 + 0, [plus](x0, x1) = x0 + x1, [0] = 0, [mark](x0) = x0, [active](x0) = x0, [and](x0, x1) = 2x0 + 5x1 + 0, [tt] = 2 orientation: mark#(x(X1,X2)) = 2X1 + X2 + 0 >= X2 + 0 = mark#(X2) mark#(and(X1,X2)) = 2X1 + 5X2 + 0 >= X1 + 0 = mark#(X1) mark#(and(X1,X2)) = 2X1 + 5X2 + 0 >= 2X1 + 5X2 + 0 = active#(and(mark(X1),X2)) active#(and(tt(),X)) = 5X + 4 >= X + 0 = mark#(X) mark#(plus(X1,X2)) = X1 + X2 + 0 >= X2 + 0 = mark#(X2) mark#(plus(X1,X2)) = X1 + X2 + 0 >= X1 + 0 = mark#(X1) mark#(plus(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = active#(plus(mark(X1),mark(X2))) active#(plus(N,0())) = N + 0 >= N + 0 = mark#(N) mark#(s(X)) = X + 0 >= X + 0 = mark#(X) mark#(x(X1,X2)) = 2X1 + X2 + 0 >= X1 + 0 = mark#(X1) mark#(x(X1,X2)) = 2X1 + X2 + 0 >= 2X1 + X2 + 0 = active#(x(mark(X1),mark(X2))) active#(x(N,s(M))) = M + 2N + 0 >= M + 2N + 0 = mark#(plus(x(N,M),N)) active#(plus(N,s(M))) = M + N + 0 >= M + N + 0 = mark#(s(plus(N,M))) active(and(tt(),X)) = 5X + 4 >= X = mark(X) active(plus(N,0())) = N + 0 >= N = mark(N) active(plus(N,s(M))) = M + N + 0 >= M + N + 0 = mark(s(plus(N,M))) active(x(N,0())) = 2N + 0 >= 0 = mark(0()) active(x(N,s(M))) = M + 2N + 0 >= M + 2N = mark(plus(x(N,M),N)) mark(and(X1,X2)) = 2X1 + 5X2 + 0 >= 2X1 + 5X2 + 0 = active(and(mark(X1),X2)) mark(tt()) = 2 >= 2 = active(tt()) mark(plus(X1,X2)) = X1 + X2 >= X1 + X2 = active(plus(mark(X1),mark(X2))) mark(0()) = 0 >= 0 = active(0()) mark(s(X)) = X + 0 >= X + 0 = active(s(mark(X))) mark(x(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = active(x(mark(X1),mark(X2))) and(mark(X1),X2) = 2X1 + 5X2 + 0 >= 2X1 + 5X2 + 0 = and(X1,X2) and(X1,mark(X2)) = 2X1 + 5X2 + 0 >= 2X1 + 5X2 + 0 = and(X1,X2) and(active(X1),X2) = 2X1 + 5X2 + 0 >= 2X1 + 5X2 + 0 = and(X1,X2) and(X1,active(X2)) = 2X1 + 5X2 + 0 >= 2X1 + 5X2 + 0 = and(X1,X2) plus(mark(X1),X2) = X1 + X2 >= X1 + X2 = plus(X1,X2) plus(X1,mark(X2)) = X1 + X2 >= X1 + X2 = plus(X1,X2) plus(active(X1),X2) = X1 + X2 >= X1 + X2 = plus(X1,X2) plus(X1,active(X2)) = X1 + X2 >= X1 + X2 = plus(X1,X2) s(mark(X)) = X + 0 >= X + 0 = s(X) s(active(X)) = X + 0 >= X + 0 = s(X) x(mark(X1),X2) = 2X1 + X2 >= 2X1 + X2 = x(X1,X2) x(X1,mark(X2)) = 2X1 + X2 >= 2X1 + X2 = x(X1,X2) x(active(X1),X2) = 2X1 + X2 >= 2X1 + X2 = x(X1,X2) x(X1,active(X2)) = 2X1 + X2 >= 2X1 + X2 = x(X1,X2) problem: DPs: mark#(x(X1,X2)) -> mark#(X2) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(plus(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(plus(N,0())) -> mark#(N) mark#(s(X)) -> mark#(X) mark#(x(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) TRS: active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(plus(x(N,M),N)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) SCC Processor: #sccs: 1 #rules: 11 #arcs: 80/144 DPs: mark#(x(X1,X2)) -> mark#(X2) mark#(and(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(plus(N,0())) -> mark#(N) mark#(s(X)) -> mark#(X) mark#(x(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) TRS: active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(plus(x(N,M),N)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) Arctic Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0 + 0, [x](x0, x1) = 7x0 + x1 + 0, [s](x0) = x0 + 0, [plus](x0, x1) = x0 + x1 + 0, [0] = 0, [mark](x0) = x0, [active](x0) = x0 + 0, [and](x0, x1) = x0 + x1 + 0, [tt] = 0 orientation: mark#(x(X1,X2)) = 7X1 + X2 + 0 >= X2 = mark#(X2) mark#(and(X1,X2)) = X1 + X2 + 0 >= X1 = mark#(X1) mark#(plus(X1,X2)) = X1 + X2 + 0 >= X2 = mark#(X2) mark#(plus(X1,X2)) = X1 + X2 + 0 >= X1 = mark#(X1) mark#(plus(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = active#(plus(mark(X1),mark(X2))) active#(plus(N,0())) = N + 0 >= N = mark#(N) mark#(s(X)) = X + 0 >= X = mark#(X) mark#(x(X1,X2)) = 7X1 + X2 + 0 >= X1 = mark#(X1) mark#(x(X1,X2)) = 7X1 + X2 + 0 >= 7X1 + X2 + 0 = active#(x(mark(X1),mark(X2))) active#(x(N,s(M))) = M + 7N + 0 >= M + 7N + 0 = mark#(plus(x(N,M),N)) active#(plus(N,s(M))) = M + N + 0 >= M + N + 0 = mark#(s(plus(N,M))) active(and(tt(),X)) = X + 0 >= X = mark(X) active(plus(N,0())) = N + 0 >= N = mark(N) active(plus(N,s(M))) = M + N + 0 >= M + N + 0 = mark(s(plus(N,M))) active(x(N,0())) = 7N + 0 >= 0 = mark(0()) active(x(N,s(M))) = M + 7N + 0 >= M + 7N + 0 = mark(plus(x(N,M),N)) mark(and(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = active(and(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(plus(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = active(plus(mark(X1),mark(X2))) mark(0()) = 0 >= 0 = active(0()) mark(s(X)) = X + 0 >= X + 0 = active(s(mark(X))) mark(x(X1,X2)) = 7X1 + X2 + 0 >= 7X1 + X2 + 0 = active(x(mark(X1),mark(X2))) and(mark(X1),X2) = X1 + X2 + 0 >= X1 + X2 + 0 = and(X1,X2) and(X1,mark(X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = and(X1,X2) and(active(X1),X2) = X1 + X2 + 0 >= X1 + X2 + 0 = and(X1,X2) and(X1,active(X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = and(X1,X2) plus(mark(X1),X2) = X1 + X2 + 0 >= X1 + X2 + 0 = plus(X1,X2) plus(X1,mark(X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = plus(X1,X2) plus(active(X1),X2) = X1 + X2 + 0 >= X1 + X2 + 0 = plus(X1,X2) plus(X1,active(X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = plus(X1,X2) s(mark(X)) = X + 0 >= X + 0 = s(X) s(active(X)) = X + 0 >= X + 0 = s(X) x(mark(X1),X2) = 7X1 + X2 + 0 >= 7X1 + X2 + 0 = x(X1,X2) x(X1,mark(X2)) = 7X1 + X2 + 0 >= 7X1 + X2 + 0 = x(X1,X2) x(active(X1),X2) = 7X1 + X2 + 7 >= 7X1 + X2 + 0 = x(X1,X2) x(X1,active(X2)) = 7X1 + X2 + 0 >= 7X1 + X2 + 0 = x(X1,X2) problem: DPs: mark#(x(X1,X2)) -> mark#(X2) mark#(and(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(plus(N,0())) -> mark#(N) mark#(s(X)) -> mark#(X) mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) TRS: active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(plus(x(N,M),N)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) Arctic Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0 + 0, [active#](x0) = x0 + 0, [x](x0, x1) = x0 + x1, [s](x0) = x0, [plus](x0, x1) = x0 + x1 + 0, [0] = 0, [mark](x0) = x0 + 0, [active](x0) = x0 + 0, [and](x0, x1) = 3x0 + 2x1 + 4, [tt] = 4 orientation: mark#(x(X1,X2)) = X1 + X2 + 0 >= X2 + 0 = mark#(X2) mark#(and(X1,X2)) = 3X1 + 2X2 + 4 >= X1 + 0 = mark#(X1) mark#(plus(X1,X2)) = X1 + X2 + 0 >= X2 + 0 = mark#(X2) mark#(plus(X1,X2)) = X1 + X2 + 0 >= X1 + 0 = mark#(X1) mark#(plus(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = active#(plus(mark(X1),mark(X2))) active#(plus(N,0())) = N + 0 >= N + 0 = mark#(N) mark#(s(X)) = X + 0 >= X + 0 = mark#(X) mark#(x(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = active#(x(mark(X1),mark(X2))) active#(x(N,s(M))) = M + N + 0 >= M + N + 0 = mark#(plus(x(N,M),N)) active#(plus(N,s(M))) = M + N + 0 >= M + N + 0 = mark#(s(plus(N,M))) active(and(tt(),X)) = 2X + 7 >= X + 0 = mark(X) active(plus(N,0())) = N + 0 >= N + 0 = mark(N) active(plus(N,s(M))) = M + N + 0 >= M + N + 0 = mark(s(plus(N,M))) active(x(N,0())) = N + 0 >= 0 = mark(0()) active(x(N,s(M))) = M + N + 0 >= M + N + 0 = mark(plus(x(N,M),N)) mark(and(X1,X2)) = 3X1 + 2X2 + 4 >= 3X1 + 2X2 + 4 = active(and(mark(X1),X2)) mark(tt()) = 4 >= 4 = active(tt()) mark(plus(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = active(plus(mark(X1),mark(X2))) mark(0()) = 0 >= 0 = active(0()) mark(s(X)) = X + 0 >= X + 0 = active(s(mark(X))) mark(x(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = active(x(mark(X1),mark(X2))) and(mark(X1),X2) = 3X1 + 2X2 + 4 >= 3X1 + 2X2 + 4 = and(X1,X2) and(X1,mark(X2)) = 3X1 + 2X2 + 4 >= 3X1 + 2X2 + 4 = and(X1,X2) and(active(X1),X2) = 3X1 + 2X2 + 4 >= 3X1 + 2X2 + 4 = and(X1,X2) and(X1,active(X2)) = 3X1 + 2X2 + 4 >= 3X1 + 2X2 + 4 = and(X1,X2) plus(mark(X1),X2) = X1 + X2 + 0 >= X1 + X2 + 0 = plus(X1,X2) plus(X1,mark(X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = plus(X1,X2) plus(active(X1),X2) = X1 + X2 + 0 >= X1 + X2 + 0 = plus(X1,X2) plus(X1,active(X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = plus(X1,X2) s(mark(X)) = X + 0 >= X = s(X) s(active(X)) = X + 0 >= X = s(X) x(mark(X1),X2) = X1 + X2 + 0 >= X1 + X2 = x(X1,X2) x(X1,mark(X2)) = X1 + X2 + 0 >= X1 + X2 = x(X1,X2) x(active(X1),X2) = X1 + X2 + 0 >= X1 + X2 = x(X1,X2) x(X1,active(X2)) = X1 + X2 + 0 >= X1 + X2 = x(X1,X2) problem: DPs: mark#(x(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(plus(N,0())) -> mark#(N) mark#(s(X)) -> mark#(X) mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) TRS: active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(plus(x(N,M),N)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) Arctic Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0 + 0, [active#](x0) = x0 + 0, [x](x0, x1) = 6x0 + 2x1 + 6, [s](x0) = x0 + 4, [plus](x0, x1) = x0 + x1, [0] = 0, [mark](x0) = x0 + 0, [active](x0) = x0 + 0, [and](x0, x1) = x0 + 6x1, [tt] = 6 orientation: mark#(x(X1,X2)) = 6X1 + 2X2 + 6 >= X2 + 0 = mark#(X2) mark#(plus(X1,X2)) = X1 + X2 + 0 >= X2 + 0 = mark#(X2) mark#(plus(X1,X2)) = X1 + X2 + 0 >= X1 + 0 = mark#(X1) mark#(plus(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = active#(plus(mark(X1),mark(X2))) active#(plus(N,0())) = N + 0 >= N + 0 = mark#(N) mark#(s(X)) = X + 4 >= X + 0 = mark#(X) mark#(x(X1,X2)) = 6X1 + 2X2 + 6 >= 6X1 + 2X2 + 6 = active#(x(mark(X1),mark(X2))) active#(x(N,s(M))) = 2M + 6N + 6 >= 2M + 6N + 6 = mark#(plus(x(N,M),N)) active#(plus(N,s(M))) = M + N + 4 >= M + N + 4 = mark#(s(plus(N,M))) active(and(tt(),X)) = 6X + 6 >= X + 0 = mark(X) active(plus(N,0())) = N + 0 >= N + 0 = mark(N) active(plus(N,s(M))) = M + N + 4 >= M + N + 4 = mark(s(plus(N,M))) active(x(N,0())) = 6N + 6 >= 0 = mark(0()) active(x(N,s(M))) = 2M + 6N + 6 >= 2M + 6N + 6 = mark(plus(x(N,M),N)) mark(and(X1,X2)) = X1 + 6X2 + 0 >= X1 + 6X2 + 0 = active(and(mark(X1),X2)) mark(tt()) = 6 >= 6 = active(tt()) mark(plus(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = active(plus(mark(X1),mark(X2))) mark(0()) = 0 >= 0 = active(0()) mark(s(X)) = X + 4 >= X + 4 = active(s(mark(X))) mark(x(X1,X2)) = 6X1 + 2X2 + 6 >= 6X1 + 2X2 + 6 = active(x(mark(X1),mark(X2))) and(mark(X1),X2) = X1 + 6X2 + 0 >= X1 + 6X2 = and(X1,X2) and(X1,mark(X2)) = X1 + 6X2 + 6 >= X1 + 6X2 = and(X1,X2) and(active(X1),X2) = X1 + 6X2 + 0 >= X1 + 6X2 = and(X1,X2) and(X1,active(X2)) = X1 + 6X2 + 6 >= X1 + 6X2 = and(X1,X2) plus(mark(X1),X2) = X1 + X2 + 0 >= X1 + X2 = plus(X1,X2) plus(X1,mark(X2)) = X1 + X2 + 0 >= X1 + X2 = plus(X1,X2) plus(active(X1),X2) = X1 + X2 + 0 >= X1 + X2 = plus(X1,X2) plus(X1,active(X2)) = X1 + X2 + 0 >= X1 + X2 = plus(X1,X2) s(mark(X)) = X + 4 >= X + 4 = s(X) s(active(X)) = X + 4 >= X + 4 = s(X) x(mark(X1),X2) = 6X1 + 2X2 + 6 >= 6X1 + 2X2 + 6 = x(X1,X2) x(X1,mark(X2)) = 6X1 + 2X2 + 6 >= 6X1 + 2X2 + 6 = x(X1,X2) x(active(X1),X2) = 6X1 + 2X2 + 6 >= 6X1 + 2X2 + 6 = x(X1,X2) x(X1,active(X2)) = 6X1 + 2X2 + 6 >= 6X1 + 2X2 + 6 = x(X1,X2) problem: DPs: mark#(plus(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(plus(N,0())) -> mark#(N) mark#(s(X)) -> mark#(X) mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) TRS: active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(plus(x(N,M),N)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) Arctic Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0, [x](x0, x1) = 4x0 + x1, [s](x0) = x0, [plus](x0, x1) = x0 + 2x1, [0] = 1, [mark](x0) = x0, [active](x0) = x0, [and](x0, x1) = x0 + x1 + 0, [tt] = 1 orientation: mark#(plus(X1,X2)) = X1 + 2X2 >= X2 = mark#(X2) mark#(plus(X1,X2)) = X1 + 2X2 >= X1 = mark#(X1) mark#(plus(X1,X2)) = X1 + 2X2 >= X1 + 2X2 = active#(plus(mark(X1),mark(X2))) active#(plus(N,0())) = N + 3 >= N = mark#(N) mark#(s(X)) = X >= X = mark#(X) mark#(x(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = active#(x(mark(X1),mark(X2))) active#(x(N,s(M))) = M + 4N >= M + 4N = mark#(plus(x(N,M),N)) active#(plus(N,s(M))) = 2M + N >= 2M + N = mark#(s(plus(N,M))) active(and(tt(),X)) = X + 1 >= X = mark(X) active(plus(N,0())) = N + 3 >= N = mark(N) active(plus(N,s(M))) = 2M + N >= 2M + N = mark(s(plus(N,M))) active(x(N,0())) = 4N + 1 >= 1 = mark(0()) active(x(N,s(M))) = M + 4N >= M + 4N = mark(plus(x(N,M),N)) mark(and(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = active(and(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(plus(X1,X2)) = X1 + 2X2 >= X1 + 2X2 = active(plus(mark(X1),mark(X2))) mark(0()) = 1 >= 1 = active(0()) mark(s(X)) = X >= X = active(s(mark(X))) mark(x(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = active(x(mark(X1),mark(X2))) and(mark(X1),X2) = X1 + X2 + 0 >= X1 + X2 + 0 = and(X1,X2) and(X1,mark(X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = and(X1,X2) and(active(X1),X2) = X1 + X2 + 0 >= X1 + X2 + 0 = and(X1,X2) and(X1,active(X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = and(X1,X2) plus(mark(X1),X2) = X1 + 2X2 >= X1 + 2X2 = plus(X1,X2) plus(X1,mark(X2)) = X1 + 2X2 >= X1 + 2X2 = plus(X1,X2) plus(active(X1),X2) = X1 + 2X2 >= X1 + 2X2 = plus(X1,X2) plus(X1,active(X2)) = X1 + 2X2 >= X1 + 2X2 = plus(X1,X2) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) x(mark(X1),X2) = 4X1 + X2 >= 4X1 + X2 = x(X1,X2) x(X1,mark(X2)) = 4X1 + X2 >= 4X1 + X2 = x(X1,X2) x(active(X1),X2) = 4X1 + X2 >= 4X1 + X2 = x(X1,X2) x(X1,active(X2)) = 4X1 + X2 >= 4X1 + X2 = x(X1,X2) problem: DPs: mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(plus(N,0())) -> mark#(N) mark#(s(X)) -> mark#(X) mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) active#(x(N,s(M))) -> mark#(plus(x(N,M),N)) active#(plus(N,s(M))) -> mark#(s(plus(N,M))) TRS: active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(plus(x(N,M),N)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) LPO Processor: argument filtering: pi(tt) = [] pi(and) = 1 pi(active) = 0 pi(mark) = 0 pi(0) = [] pi(plus) = [0,1] pi(s) = [0] pi(x) = [0,1] pi(active#) = 0 pi(mark#) = 0 precedence: x > plus > mark# ~ active# ~ s ~ 0 ~ mark ~ active ~ and ~ tt problem: DPs: mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) TRS: active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(plus(x(N,M),N)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) SCC Processor: #sccs: 0 #rules: 0 #arcs: 63/4 DPs: plus#(mark(X1),X2) -> plus#(X1,X2) plus#(X1,mark(X2)) -> plus#(X1,X2) plus#(active(X1),X2) -> plus#(X1,X2) plus#(X1,active(X2)) -> plus#(X1,X2) TRS: active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(plus(x(N,M),N)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) Subterm Criterion Processor: simple projection: pi(plus#) = 1 problem: DPs: plus#(mark(X1),X2) -> plus#(X1,X2) plus#(active(X1),X2) -> plus#(X1,X2) TRS: active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(plus(x(N,M),N)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) Subterm Criterion Processor: simple projection: pi(plus#) = 0 problem: DPs: TRS: active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(plus(x(N,M),N)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) Qed DPs: s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) TRS: active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(plus(x(N,M),N)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) Subterm Criterion Processor: simple projection: pi(s#) = 0 problem: DPs: TRS: active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(plus(x(N,M),N)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) Qed DPs: x#(mark(X1),X2) -> x#(X1,X2) x#(X1,mark(X2)) -> x#(X1,X2) x#(active(X1),X2) -> x#(X1,X2) x#(X1,active(X2)) -> x#(X1,X2) TRS: active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(plus(x(N,M),N)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) Subterm Criterion Processor: simple projection: pi(x#) = 1 problem: DPs: x#(mark(X1),X2) -> x#(X1,X2) x#(active(X1),X2) -> x#(X1,X2) TRS: active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(plus(x(N,M),N)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) Subterm Criterion Processor: simple projection: pi(x#) = 0 problem: DPs: TRS: active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(plus(x(N,M),N)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) Qed DPs: and#(mark(X1),X2) -> and#(X1,X2) and#(X1,mark(X2)) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) TRS: active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(plus(x(N,M),N)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) Subterm Criterion Processor: simple projection: pi(and#) = 1 problem: DPs: and#(mark(X1),X2) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) TRS: active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(plus(x(N,M),N)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) Subterm Criterion Processor: simple projection: pi(and#) = 0 problem: DPs: TRS: active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) active(x(N,0())) -> mark(0()) active(x(N,s(M))) -> mark(plus(x(N,M),N)) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(tt()) -> active(tt()) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) Qed