/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: 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#(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#(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#(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#(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) 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,0())) -> mark#(0()) -> mark#(0()) -> active#(0()) 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,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))) SCC Processor: #sccs: 1 #rules: 13 #arcs: 107/289 DPs: mark#(x(X1,X2)) -> mark#(X2) mark#(x(X1,X2)) -> active#(x(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#(plus(N,s(M))) -> mark#(s(plus(N,M))) mark#(s(X)) -> mark#(X) mark#(x(X1,X2)) -> mark#(X1) 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) active#(plus(N,0())) -> mark#(N) 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 usable rules: 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) interpretation: [mark#](x0) = x0, [active#](x0) = x0 + 0, [x](x0, x1) = x0 + x1 + 0, [s](x0) = x0 + 1, [plus](x0, x1) = x0 + x1 + 1, [0] = 0, [mark](x0) = x0, [active](x0) = x0 + 0, [and](x0, x1) = 7x0 + x1 + 7, [tt] = 0 orientation: mark#(x(X1,X2)) = X1 + X2 + 0 >= X2 = mark#(X2) mark#(x(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = active#(x(mark(X1),mark(X2))) active#(x(N,s(M))) = M + N + 1 >= M + N + 1 = mark#(plus(x(N,M),N)) mark#(plus(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active#(plus(mark(X1),mark(X2))) active#(plus(N,s(M))) = M + N + 1 >= M + N + 1 = mark#(s(plus(N,M))) mark#(s(X)) = X + 1 >= X = mark#(X) mark#(x(X1,X2)) = X1 + X2 + 0 >= X1 = mark#(X1) mark#(plus(X1,X2)) = X1 + X2 + 1 >= X1 = mark#(X1) mark#(plus(X1,X2)) = X1 + X2 + 1 >= X2 = mark#(X2) mark#(and(X1,X2)) = 7X1 + X2 + 7 >= 7X1 + X2 + 7 = active#(and(mark(X1),X2)) active#(and(tt(),X)) = X + 7 >= X = mark#(X) mark#(and(X1,X2)) = 7X1 + X2 + 7 >= X1 = mark#(X1) active#(plus(N,0())) = N + 1 >= N = mark#(N) active(and(tt(),X)) = X + 7 >= X = mark(X) active(plus(N,0())) = N + 1 >= N = mark(N) active(plus(N,s(M))) = M + N + 1 >= M + N + 1 = mark(s(plus(N,M))) active(x(N,0())) = N + 0 >= 0 = mark(0()) active(x(N,s(M))) = M + N + 1 >= M + N + 1 = mark(plus(x(N,M),N)) mark(and(X1,X2)) = 7X1 + X2 + 7 >= 7X1 + X2 + 7 = active(and(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(plus(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(plus(mark(X1),mark(X2))) mark(0()) = 0 >= 0 = active(0()) mark(s(X)) = X + 1 >= X + 1 = active(s(mark(X))) mark(x(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = active(x(mark(X1),mark(X2))) and(mark(X1),X2) = 7X1 + X2 + 7 >= 7X1 + X2 + 7 = and(X1,X2) and(X1,mark(X2)) = 7X1 + X2 + 7 >= 7X1 + X2 + 7 = and(X1,X2) and(active(X1),X2) = 7X1 + X2 + 7 >= 7X1 + X2 + 7 = and(X1,X2) and(X1,active(X2)) = 7X1 + X2 + 7 >= 7X1 + X2 + 7 = and(X1,X2) plus(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = plus(X1,X2) plus(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = plus(X1,X2) plus(active(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = plus(X1,X2) plus(X1,active(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = plus(X1,X2) s(mark(X)) = X + 1 >= X + 1 = s(X) s(active(X)) = X + 1 >= X + 1 = s(X) x(mark(X1),X2) = X1 + X2 + 0 >= X1 + X2 + 0 = x(X1,X2) x(X1,mark(X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = x(X1,X2) x(active(X1),X2) = X1 + X2 + 0 >= X1 + X2 + 0 = x(X1,X2) x(X1,active(X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = x(X1,X2) problem: DPs: mark#(x(X1,X2)) -> mark#(X2) mark#(x(X1,X2)) -> active#(x(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#(plus(N,s(M))) -> mark#(s(plus(N,M))) mark#(s(X)) -> mark#(X) mark#(x(X1,X2)) -> mark#(X1) 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) active#(plus(N,0())) -> mark#(N) 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) Restore Modifier: DPs: mark#(x(X1,X2)) -> mark#(X2) mark#(x(X1,X2)) -> active#(x(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#(plus(N,s(M))) -> mark#(s(plus(N,M))) mark#(s(X)) -> mark#(X) mark#(x(X1,X2)) -> mark#(X1) 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) active#(plus(N,0())) -> mark#(N) 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 usable rules: 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) interpretation: [mark#](x0) = x0, [active#](x0) = x0 + 0, [x](x0, x1) = 7x0 + x1 + 0, [s](x0) = x0 + 5, [plus](x0, x1) = x0 + x1 + 5, [0] = 0, [mark](x0) = x0, [active](x0) = x0, [and](x0, x1) = x0 + x1 + 5, [tt] = 0 orientation: mark#(x(X1,X2)) = 7X1 + X2 + 0 >= X2 = mark#(X2) mark#(x(X1,X2)) = 7X1 + X2 + 0 >= 7X1 + X2 + 0 = active#(x(mark(X1),mark(X2))) active#(x(N,s(M))) = M + 7N + 5 >= M + 7N + 5 = mark#(plus(x(N,M),N)) mark#(plus(X1,X2)) = X1 + X2 + 5 >= X1 + X2 + 5 = active#(plus(mark(X1),mark(X2))) active#(plus(N,s(M))) = M + N + 5 >= M + N + 5 = mark#(s(plus(N,M))) mark#(s(X)) = X + 5 >= X = mark#(X) mark#(x(X1,X2)) = 7X1 + X2 + 0 >= X1 = mark#(X1) mark#(plus(X1,X2)) = X1 + X2 + 5 >= X1 = mark#(X1) mark#(plus(X1,X2)) = X1 + X2 + 5 >= X2 = mark#(X2) mark#(and(X1,X2)) = X1 + X2 + 5 >= X1 + X2 + 5 = active#(and(mark(X1),X2)) active#(and(tt(),X)) = X + 5 >= X = mark#(X) active#(plus(N,0())) = N + 5 >= N = mark#(N) active(and(tt(),X)) = X + 5 >= X = mark(X) active(plus(N,0())) = N + 5 >= N = mark(N) active(plus(N,s(M))) = M + N + 5 >= M + N + 5 = mark(s(plus(N,M))) active(x(N,0())) = 7N + 0 >= 0 = mark(0()) active(x(N,s(M))) = M + 7N + 5 >= M + 7N + 5 = mark(plus(x(N,M),N)) mark(and(X1,X2)) = X1 + X2 + 5 >= X1 + X2 + 5 = active(and(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(plus(X1,X2)) = X1 + X2 + 5 >= X1 + X2 + 5 = active(plus(mark(X1),mark(X2))) mark(0()) = 0 >= 0 = active(0()) mark(s(X)) = X + 5 >= X + 5 = 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 + 5 >= X1 + X2 + 5 = and(X1,X2) and(X1,mark(X2)) = X1 + X2 + 5 >= X1 + X2 + 5 = and(X1,X2) and(active(X1),X2) = X1 + X2 + 5 >= X1 + X2 + 5 = and(X1,X2) and(X1,active(X2)) = X1 + X2 + 5 >= X1 + X2 + 5 = and(X1,X2) plus(mark(X1),X2) = X1 + X2 + 5 >= X1 + X2 + 5 = plus(X1,X2) plus(X1,mark(X2)) = X1 + X2 + 5 >= X1 + X2 + 5 = plus(X1,X2) plus(active(X1),X2) = X1 + X2 + 5 >= X1 + X2 + 5 = plus(X1,X2) plus(X1,active(X2)) = X1 + X2 + 5 >= X1 + X2 + 5 = plus(X1,X2) s(mark(X)) = X + 5 >= X + 5 = s(X) s(active(X)) = X + 5 >= X + 5 = 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 + 0 >= 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#(x(X1,X2)) -> active#(x(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#(plus(N,s(M))) -> mark#(s(plus(N,M))) mark#(s(X)) -> mark#(X) 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) active#(plus(N,0())) -> mark#(N) 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) Restore Modifier: DPs: mark#(x(X1,X2)) -> mark#(X2) mark#(x(X1,X2)) -> active#(x(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#(plus(N,s(M))) -> mark#(s(plus(N,M))) mark#(s(X)) -> mark#(X) 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) active#(plus(N,0())) -> mark#(N) 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 usable rules: 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) precedence: x > plus > mark# ~ active# ~ s ~ 0 ~ mark ~ active ~ and ~ tt problem: DPs: mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(and(tt(),X)) -> mark#(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) Restore Modifier: DPs: mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(and(tt(),X)) -> mark#(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) SCC Processor: #sccs: 1 #rules: 2 #arcs: 80/16 DPs: mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(and(tt(),X)) -> mark#(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(and) = [1,1] pi(s) = [0,0] pi(x) = [0,0] pi(active#) = 0 pi(mark#) = [0,0] problem: DPs: active#(and(tt(),X)) -> mark#(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) SCC Processor: #sccs: 0 #rules: 0 #arcs: 2/1 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#) = 0 problem: DPs: plus#(X1,mark(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: 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#) = 0 problem: DPs: x#(X1,mark(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: 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#) = 0 problem: DPs: and#(X1,mark(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: 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