YES Problem: active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) 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))) 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) 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))) 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))) 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) TRS: active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) 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))) 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) 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))) 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))) 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) TRS: active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) 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))) 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) 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) 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#(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#(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#(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#(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#(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#(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#(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#(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#(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#(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#(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#(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#(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#(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) EDG 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))) 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))) 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) TRS: active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) 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))) 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) graph: and#(mark(X1),X2) -> and#(X1,X2) -> and#(mark(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#(active(X1),X2) -> and#(X1,X2) and#(mark(X1),X2) -> and#(X1,X2) -> and#(X1,active(X2)) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) -> and#(mark(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#(active(X1),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#(mark(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#(active(X1),X2) -> and#(X1,X2) and#(X1,mark(X2)) -> and#(X1,X2) -> and#(X1,active(X2)) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) -> and#(mark(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#(active(X1),X2) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) -> and#(X1,active(X2)) -> and#(X1,X2) s#(mark(X)) -> s#(X) -> s#(mark(X)) -> s#(X) s#(mark(X)) -> s#(X) -> s#(active(X)) -> s#(X) s#(active(X)) -> s#(X) -> s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) -> s#(active(X)) -> s#(X) plus#(mark(X1),X2) -> plus#(X1,X2) -> plus#(mark(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#(active(X1),X2) -> plus#(X1,X2) plus#(mark(X1),X2) -> plus#(X1,X2) -> plus#(X1,active(X2)) -> plus#(X1,X2) plus#(active(X1),X2) -> plus#(X1,X2) -> plus#(mark(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#(active(X1),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#(mark(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#(active(X1),X2) -> plus#(X1,X2) plus#(X1,mark(X2)) -> plus#(X1,X2) -> plus#(X1,active(X2)) -> plus#(X1,X2) plus#(X1,active(X2)) -> plus#(X1,X2) -> plus#(mark(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#(active(X1),X2) -> plus#(X1,X2) plus#(X1,active(X2)) -> plus#(X1,X2) -> plus#(X1,active(X2)) -> plus#(X1,X2) mark#(s(X)) -> s#(mark(X)) -> s#(mark(X)) -> s#(X) mark#(s(X)) -> s#(mark(X)) -> s#(active(X)) -> s#(X) mark#(s(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) 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)) -> plus#(mark(X1),mark(X2)) 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)) -> s#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(mark(X))) 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))) -> 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))) -> mark#(s(plus(N,M))) mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) -> plus#(mark(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#(active(X1),X2) -> plus#(X1,X2) mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) -> plus#(X1,active(X2)) -> plus#(X1,X2) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) 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)) -> plus#(mark(X1),mark(X2)) 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)) -> s#(mark(X)) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> active#(s(mark(X))) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) 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)) -> plus#(mark(X1),mark(X2)) 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)) -> s#(mark(X)) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> active#(s(mark(X))) 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))) -> 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))) -> mark#(s(plus(N,M))) mark#(and(X1,X2)) -> and#(mark(X1),X2) -> and#(mark(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#(active(X1),X2) -> and#(X1,X2) mark#(and(X1,X2)) -> and#(mark(X1),X2) -> and#(X1,active(X2)) -> and#(X1,X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) 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)) -> plus#(mark(X1),mark(X2)) 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)) -> s#(mark(X)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> active#(s(mark(X))) 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))) -> 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))) -> mark#(s(plus(N,M))) active#(plus(N,s(M))) -> s#(plus(N,M)) -> s#(mark(X)) -> s#(X) active#(plus(N,s(M))) -> s#(plus(N,M)) -> s#(active(X)) -> s#(X) active#(plus(N,s(M))) -> plus#(N,M) -> plus#(mark(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#(active(X1),X2) -> plus#(X1,X2) active#(plus(N,s(M))) -> plus#(N,M) -> plus#(X1,active(X2)) -> plus#(X1,X2) 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)) -> 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))) -> 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)) -> 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))) -> mark#(s(plus(N,M))) -> mark#(s(X)) -> 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)) -> active#(s(mark(X))) active#(plus(N,0())) -> mark#(N) -> mark#(and(X1,X2)) -> mark#(X1) active#(plus(N,0())) -> mark#(N) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) 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)) -> plus#(mark(X1),mark(X2)) 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)) -> s#(mark(X)) active#(plus(N,0())) -> mark#(N) -> mark#(s(X)) -> active#(s(mark(X))) active#(and(tt(),X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) active#(and(tt(),X)) -> mark#(X) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) 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)) -> plus#(mark(X1),mark(X2)) 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)) -> s#(mark(X)) active#(and(tt(),X)) -> mark#(X) -> mark#(s(X)) -> active#(s(mark(X))) SCC Processor: #sccs: 4 #rules: 20 #arcs: 149/729 DPs: mark#(s(X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) 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#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X2) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(and(tt(),X)) -> mark#(X) mark#(and(X1,X2)) -> mark#(X1) TRS: active(and(tt(),X)) -> mark(X) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(s(plus(N,M))) 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))) 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) Matrix Interpretation Processor: dim=1 interpretation: [mark#](x0) = 2x0 + 5, [active#](x0) = 2x0 + 4, [s](x0) = x0 + 1, [plus](x0, x1) = 4x0 + 2x1 + 1, [0] = 0, [mark](x0) = x0, [active](x0) = x0, [and](x0, x1) = 4x0 + 2x1 + 1, [tt] = 2 orientation: mark#(s(X)) = 2X + 7 >= 2X + 5 = mark#(X) mark#(s(X)) = 2X + 7 >= 2X + 6 = active#(s(mark(X))) active#(plus(N,s(M))) = 4M + 8N + 10 >= 4M + 8N + 9 = mark#(s(plus(N,M))) mark#(plus(X1,X2)) = 8X1 + 4X2 + 7 >= 8X1 + 4X2 + 6 = active#(plus(mark(X1),mark(X2))) active#(plus(N,0())) = 8N + 6 >= 2N + 5 = mark#(N) mark#(plus(X1,X2)) = 8X1 + 4X2 + 7 >= 2X1 + 5 = mark#(X1) mark#(plus(X1,X2)) = 8X1 + 4X2 + 7 >= 2X2 + 5 = mark#(X2) mark#(and(X1,X2)) = 8X1 + 4X2 + 7 >= 8X1 + 4X2 + 6 = active#(and(mark(X1),X2)) active#(and(tt(),X)) = 4X + 22 >= 2X + 5 = mark#(X) mark#(and(X1,X2)) = 8X1 + 4X2 + 7 >= 2X1 + 5 = mark#(X1) active(and(tt(),X)) = 2X + 9 >= X = mark(X) active(plus(N,0())) = 4N + 1 >= N = mark(N) active(plus(N,s(M))) = 2M + 4N + 3 >= 2M + 4N + 2 = mark(s(plus(N,M))) mark(and(X1,X2)) = 4X1 + 2X2 + 1 >= 4X1 + 2X2 + 1 = active(and(mark(X1),X2)) mark(tt()) = 2 >= 2 = active(tt()) mark(plus(X1,X2)) = 4X1 + 2X2 + 1 >= 4X1 + 2X2 + 1 = active(plus(mark(X1),mark(X2))) mark(0()) = 0 >= 0 = active(0()) mark(s(X)) = X + 1 >= X + 1 = active(s(mark(X))) and(mark(X1),X2) = 4X1 + 2X2 + 1 >= 4X1 + 2X2 + 1 = and(X1,X2) and(X1,mark(X2)) = 4X1 + 2X2 + 1 >= 4X1 + 2X2 + 1 = and(X1,X2) and(active(X1),X2) = 4X1 + 2X2 + 1 >= 4X1 + 2X2 + 1 = and(X1,X2) and(X1,active(X2)) = 4X1 + 2X2 + 1 >= 4X1 + 2X2 + 1 = and(X1,X2) plus(mark(X1),X2) = 4X1 + 2X2 + 1 >= 4X1 + 2X2 + 1 = plus(X1,X2) plus(X1,mark(X2)) = 4X1 + 2X2 + 1 >= 4X1 + 2X2 + 1 = plus(X1,X2) plus(active(X1),X2) = 4X1 + 2X2 + 1 >= 4X1 + 2X2 + 1 = plus(X1,X2) plus(X1,active(X2)) = 4X1 + 2X2 + 1 >= 4X1 + 2X2 + 1 = plus(X1,X2) s(mark(X)) = X + 1 >= X + 1 = s(X) s(active(X)) = X + 1 >= X + 1 = s(X) 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))) 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))) 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) Qed DPs: plus#(mark(X1),X2) -> plus#(X1,X2) plus#(X1,active(X2)) -> plus#(X1,X2) plus#(active(X1),X2) -> plus#(X1,X2) plus#(X1,mark(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))) 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))) 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) Matrix Interpretation Processor: dim=1 interpretation: [plus#](x0, x1) = 4x0 + x1, [s](x0) = 2, [plus](x0, x1) = 4x0 + 2x1 + 4, [0] = 2, [mark](x0) = 4x0 + 2, [active](x0) = x0 + 2, [and](x0, x1) = 4x1 + 6, [tt] = 6 orientation: plus#(mark(X1),X2) = 16X1 + X2 + 8 >= 4X1 + X2 = plus#(X1,X2) plus#(X1,active(X2)) = 4X1 + X2 + 2 >= 4X1 + X2 = plus#(X1,X2) plus#(active(X1),X2) = 4X1 + X2 + 8 >= 4X1 + X2 = plus#(X1,X2) plus#(X1,mark(X2)) = 4X1 + 4X2 + 2 >= 4X1 + X2 = plus#(X1,X2) active(and(tt(),X)) = 4X + 8 >= 4X + 2 = mark(X) active(plus(N,0())) = 4N + 10 >= 4N + 2 = mark(N) active(plus(N,s(M))) = 4N + 10 >= 10 = mark(s(plus(N,M))) mark(and(X1,X2)) = 16X2 + 26 >= 4X2 + 8 = active(and(mark(X1),X2)) mark(tt()) = 26 >= 8 = active(tt()) mark(plus(X1,X2)) = 16X1 + 8X2 + 18 >= 16X1 + 8X2 + 18 = active(plus(mark(X1),mark(X2))) mark(0()) = 10 >= 4 = active(0()) mark(s(X)) = 10 >= 4 = active(s(mark(X))) and(mark(X1),X2) = 4X2 + 6 >= 4X2 + 6 = and(X1,X2) and(X1,mark(X2)) = 16X2 + 14 >= 4X2 + 6 = and(X1,X2) and(active(X1),X2) = 4X2 + 6 >= 4X2 + 6 = and(X1,X2) and(X1,active(X2)) = 4X2 + 14 >= 4X2 + 6 = and(X1,X2) plus(mark(X1),X2) = 16X1 + 2X2 + 12 >= 4X1 + 2X2 + 4 = plus(X1,X2) plus(X1,mark(X2)) = 4X1 + 8X2 + 8 >= 4X1 + 2X2 + 4 = plus(X1,X2) plus(active(X1),X2) = 4X1 + 2X2 + 12 >= 4X1 + 2X2 + 4 = plus(X1,X2) plus(X1,active(X2)) = 4X1 + 2X2 + 8 >= 4X1 + 2X2 + 4 = plus(X1,X2) s(mark(X)) = 2 >= 2 = s(X) s(active(X)) = 2 >= 2 = s(X) 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))) 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))) 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) 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))) 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))) 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) Matrix Interpretation Processor: dim=1 interpretation: [s#](x0) = x0, [s](x0) = 2, [plus](x0, x1) = 2x0 + x1 + 2, [0] = 0, [mark](x0) = 2x0 + 1/2, [active](x0) = x0 + 1/2, [and](x0, x1) = 3x1, [tt] = 2 orientation: s#(mark(X)) = 2X + 1/2 >= X = s#(X) s#(active(X)) = X + 1/2 >= X = s#(X) active(and(tt(),X)) = 3X + 1/2 >= 2X + 1/2 = mark(X) active(plus(N,0())) = 2N + 5/2 >= 2N + 1/2 = mark(N) active(plus(N,s(M))) = 2N + 9/2 >= 9/2 = mark(s(plus(N,M))) mark(and(X1,X2)) = 6X2 + 1/2 >= 3X2 + 1/2 = active(and(mark(X1),X2)) mark(tt()) = 9/2 >= 5/2 = active(tt()) mark(plus(X1,X2)) = 4X1 + 2X2 + 9/2 >= 4X1 + 2X2 + 4 = active(plus(mark(X1),mark(X2))) mark(0()) = 1/2 >= 1/2 = active(0()) mark(s(X)) = 9/2 >= 5/2 = active(s(mark(X))) and(mark(X1),X2) = 3X2 >= 3X2 = and(X1,X2) and(X1,mark(X2)) = 6X2 + 3/2 >= 3X2 = and(X1,X2) and(active(X1),X2) = 3X2 >= 3X2 = and(X1,X2) and(X1,active(X2)) = 3X2 + 3/2 >= 3X2 = and(X1,X2) plus(mark(X1),X2) = 4X1 + X2 + 3 >= 2X1 + X2 + 2 = plus(X1,X2) plus(X1,mark(X2)) = 2X1 + 2X2 + 5/2 >= 2X1 + X2 + 2 = plus(X1,X2) plus(active(X1),X2) = 2X1 + X2 + 3 >= 2X1 + X2 + 2 = plus(X1,X2) plus(X1,active(X2)) = 2X1 + X2 + 5/2 >= 2X1 + X2 + 2 = plus(X1,X2) s(mark(X)) = 2 >= 2 = s(X) s(active(X)) = 2 >= 2 = s(X) 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))) 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))) 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) Qed DPs: and#(mark(X1),X2) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) and#(X1,mark(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))) 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))) 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) Matrix Interpretation Processor: dim=1 interpretation: [and#](x0, x1) = 4x0 + x1, [s](x0) = 2, [plus](x0, x1) = 4x0 + 2x1 + 4, [0] = 2, [mark](x0) = 4x0 + 2, [active](x0) = x0 + 2, [and](x0, x1) = 4x1 + 6, [tt] = 6 orientation: and#(mark(X1),X2) = 16X1 + X2 + 8 >= 4X1 + X2 = and#(X1,X2) and#(X1,active(X2)) = 4X1 + X2 + 2 >= 4X1 + X2 = and#(X1,X2) and#(active(X1),X2) = 4X1 + X2 + 8 >= 4X1 + X2 = and#(X1,X2) and#(X1,mark(X2)) = 4X1 + 4X2 + 2 >= 4X1 + X2 = and#(X1,X2) active(and(tt(),X)) = 4X + 8 >= 4X + 2 = mark(X) active(plus(N,0())) = 4N + 10 >= 4N + 2 = mark(N) active(plus(N,s(M))) = 4N + 10 >= 10 = mark(s(plus(N,M))) mark(and(X1,X2)) = 16X2 + 26 >= 4X2 + 8 = active(and(mark(X1),X2)) mark(tt()) = 26 >= 8 = active(tt()) mark(plus(X1,X2)) = 16X1 + 8X2 + 18 >= 16X1 + 8X2 + 18 = active(plus(mark(X1),mark(X2))) mark(0()) = 10 >= 4 = active(0()) mark(s(X)) = 10 >= 4 = active(s(mark(X))) and(mark(X1),X2) = 4X2 + 6 >= 4X2 + 6 = and(X1,X2) and(X1,mark(X2)) = 16X2 + 14 >= 4X2 + 6 = and(X1,X2) and(active(X1),X2) = 4X2 + 6 >= 4X2 + 6 = and(X1,X2) and(X1,active(X2)) = 4X2 + 14 >= 4X2 + 6 = and(X1,X2) plus(mark(X1),X2) = 16X1 + 2X2 + 12 >= 4X1 + 2X2 + 4 = plus(X1,X2) plus(X1,mark(X2)) = 4X1 + 8X2 + 8 >= 4X1 + 2X2 + 4 = plus(X1,X2) plus(active(X1),X2) = 4X1 + 2X2 + 12 >= 4X1 + 2X2 + 4 = plus(X1,X2) plus(X1,active(X2)) = 4X1 + 2X2 + 8 >= 4X1 + 2X2 + 4 = plus(X1,X2) s(mark(X)) = 2 >= 2 = s(X) s(active(X)) = 2 >= 2 = s(X) 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))) 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))) 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) Qed