MAYBE Problem: active(U11(tt(),N)) -> mark(N) active(U21(tt(),M,N)) -> mark(s(plus(N,M))) active(and(tt(),X)) -> mark(X) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(and(isNat(V1),isNat(V2))) active(isNat(s(V1))) -> mark(isNat(V1)) active(plus(N,0())) -> mark(U11(isNat(N),N)) active(plus(N,s(M))) -> mark(U21(and(isNat(M),isNat(N)),M,N)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(0()) -> active(0()) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) Proof: DP Processor: DPs: active#(U11(tt(),N)) -> mark#(N) active#(U21(tt(),M,N)) -> plus#(N,M) active#(U21(tt(),M,N)) -> s#(plus(N,M)) active#(U21(tt(),M,N)) -> mark#(s(plus(N,M))) active#(and(tt(),X)) -> mark#(X) active#(isNat(0())) -> mark#(tt()) active#(isNat(plus(V1,V2))) -> isNat#(V2) active#(isNat(plus(V1,V2))) -> isNat#(V1) active#(isNat(plus(V1,V2))) -> and#(isNat(V1),isNat(V2)) active#(isNat(plus(V1,V2))) -> mark#(and(isNat(V1),isNat(V2))) active#(isNat(s(V1))) -> isNat#(V1) active#(isNat(s(V1))) -> mark#(isNat(V1)) active#(plus(N,0())) -> isNat#(N) active#(plus(N,0())) -> U11#(isNat(N),N) active#(plus(N,0())) -> mark#(U11(isNat(N),N)) active#(plus(N,s(M))) -> isNat#(N) active#(plus(N,s(M))) -> isNat#(M) active#(plus(N,s(M))) -> and#(isNat(M),isNat(N)) active#(plus(N,s(M))) -> U21#(and(isNat(M),isNat(N)),M,N) active#(plus(N,s(M))) -> mark#(U21(and(isNat(M),isNat(N)),M,N)) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> U11#(mark(X1),X2) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) mark#(tt()) -> active#(tt()) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) mark#(s(X)) -> mark#(X) mark#(s(X)) -> s#(mark(X)) mark#(s(X)) -> active#(s(mark(X))) 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#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> and#(mark(X1),X2) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isNat(X)) -> active#(isNat(X)) mark#(0()) -> active#(0()) U11#(mark(X1),X2) -> U11#(X1,X2) U11#(X1,mark(X2)) -> U11#(X1,X2) U11#(active(X1),X2) -> U11#(X1,X2) U11#(X1,active(X2)) -> U11#(X1,X2) U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3) U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3) U21#(active(X1),X2,X3) -> U21#(X1,X2,X3) U21#(X1,active(X2),X3) -> U21#(X1,X2,X3) U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) 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) 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) isNat#(mark(X)) -> isNat#(X) isNat#(active(X)) -> isNat#(X) TRS: active(U11(tt(),N)) -> mark(N) active(U21(tt(),M,N)) -> mark(s(plus(N,M))) active(and(tt(),X)) -> mark(X) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(and(isNat(V1),isNat(V2))) active(isNat(s(V1))) -> mark(isNat(V1)) active(plus(N,0())) -> mark(U11(isNat(N),N)) active(plus(N,s(M))) -> mark(U21(and(isNat(M),isNat(N)),M,N)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(0()) -> active(0()) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) TDG Processor: DPs: active#(U11(tt(),N)) -> mark#(N) active#(U21(tt(),M,N)) -> plus#(N,M) active#(U21(tt(),M,N)) -> s#(plus(N,M)) active#(U21(tt(),M,N)) -> mark#(s(plus(N,M))) active#(and(tt(),X)) -> mark#(X) active#(isNat(0())) -> mark#(tt()) active#(isNat(plus(V1,V2))) -> isNat#(V2) active#(isNat(plus(V1,V2))) -> isNat#(V1) active#(isNat(plus(V1,V2))) -> and#(isNat(V1),isNat(V2)) active#(isNat(plus(V1,V2))) -> mark#(and(isNat(V1),isNat(V2))) active#(isNat(s(V1))) -> isNat#(V1) active#(isNat(s(V1))) -> mark#(isNat(V1)) active#(plus(N,0())) -> isNat#(N) active#(plus(N,0())) -> U11#(isNat(N),N) active#(plus(N,0())) -> mark#(U11(isNat(N),N)) active#(plus(N,s(M))) -> isNat#(N) active#(plus(N,s(M))) -> isNat#(M) active#(plus(N,s(M))) -> and#(isNat(M),isNat(N)) active#(plus(N,s(M))) -> U21#(and(isNat(M),isNat(N)),M,N) active#(plus(N,s(M))) -> mark#(U21(and(isNat(M),isNat(N)),M,N)) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> U11#(mark(X1),X2) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) mark#(tt()) -> active#(tt()) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) mark#(s(X)) -> mark#(X) mark#(s(X)) -> s#(mark(X)) mark#(s(X)) -> active#(s(mark(X))) 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#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> and#(mark(X1),X2) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isNat(X)) -> active#(isNat(X)) mark#(0()) -> active#(0()) U11#(mark(X1),X2) -> U11#(X1,X2) U11#(X1,mark(X2)) -> U11#(X1,X2) U11#(active(X1),X2) -> U11#(X1,X2) U11#(X1,active(X2)) -> U11#(X1,X2) U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3) U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3) U21#(active(X1),X2,X3) -> U21#(X1,X2,X3) U21#(X1,active(X2),X3) -> U21#(X1,X2,X3) U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) 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) 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) isNat#(mark(X)) -> isNat#(X) isNat#(active(X)) -> isNat#(X) TRS: active(U11(tt(),N)) -> mark(N) active(U21(tt(),M,N)) -> mark(s(plus(N,M))) active(and(tt(),X)) -> mark(X) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(and(isNat(V1),isNat(V2))) active(isNat(s(V1))) -> mark(isNat(V1)) active(plus(N,0())) -> mark(U11(isNat(N),N)) active(plus(N,s(M))) -> mark(U21(and(isNat(M),isNat(N)),M,N)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(0()) -> active(0()) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) graph: U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) -> U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3) U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) -> U21#(X1,active(X2),X3) -> U21#(X1,X2,X3) U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) -> U21#(active(X1),X2,X3) -> U21#(X1,X2,X3) U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) -> U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3) U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) -> U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3) U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) -> U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) U21#(active(X1),X2,X3) -> U21#(X1,X2,X3) -> U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3) U21#(active(X1),X2,X3) -> U21#(X1,X2,X3) -> U21#(X1,active(X2),X3) -> U21#(X1,X2,X3) U21#(active(X1),X2,X3) -> U21#(X1,X2,X3) -> U21#(active(X1),X2,X3) -> U21#(X1,X2,X3) U21#(active(X1),X2,X3) -> U21#(X1,X2,X3) -> U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3) U21#(active(X1),X2,X3) -> U21#(X1,X2,X3) -> U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3) U21#(active(X1),X2,X3) -> U21#(X1,X2,X3) -> U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3) -> U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3) U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3) -> U21#(X1,active(X2),X3) -> U21#(X1,X2,X3) U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3) -> U21#(active(X1),X2,X3) -> U21#(X1,X2,X3) U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3) -> U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3) U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3) -> U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3) U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3) -> U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) U21#(X1,active(X2),X3) -> U21#(X1,X2,X3) -> U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3) U21#(X1,active(X2),X3) -> U21#(X1,X2,X3) -> U21#(X1,active(X2),X3) -> U21#(X1,X2,X3) U21#(X1,active(X2),X3) -> U21#(X1,X2,X3) -> U21#(active(X1),X2,X3) -> U21#(X1,X2,X3) U21#(X1,active(X2),X3) -> U21#(X1,X2,X3) -> U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3) U21#(X1,active(X2),X3) -> U21#(X1,X2,X3) -> U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3) U21#(X1,active(X2),X3) -> U21#(X1,X2,X3) -> U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3) -> U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3) U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3) -> U21#(X1,active(X2),X3) -> U21#(X1,X2,X3) U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3) -> U21#(active(X1),X2,X3) -> U21#(X1,X2,X3) U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3) -> U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3) U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3) -> U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3) U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3) -> U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3) -> U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3) U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3) -> U21#(X1,active(X2),X3) -> U21#(X1,X2,X3) U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3) -> U21#(active(X1),X2,X3) -> U21#(X1,X2,X3) U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3) -> U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3) U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3) -> U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3) U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3) -> U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) U11#(mark(X1),X2) -> U11#(X1,X2) -> U11#(X1,active(X2)) -> U11#(X1,X2) U11#(mark(X1),X2) -> U11#(X1,X2) -> U11#(active(X1),X2) -> U11#(X1,X2) U11#(mark(X1),X2) -> U11#(X1,X2) -> U11#(X1,mark(X2)) -> U11#(X1,X2) U11#(mark(X1),X2) -> U11#(X1,X2) -> U11#(mark(X1),X2) -> U11#(X1,X2) U11#(active(X1),X2) -> U11#(X1,X2) -> U11#(X1,active(X2)) -> U11#(X1,X2) U11#(active(X1),X2) -> U11#(X1,X2) -> U11#(active(X1),X2) -> U11#(X1,X2) U11#(active(X1),X2) -> U11#(X1,X2) -> U11#(X1,mark(X2)) -> U11#(X1,X2) U11#(active(X1),X2) -> U11#(X1,X2) -> U11#(mark(X1),X2) -> U11#(X1,X2) U11#(X1,mark(X2)) -> U11#(X1,X2) -> U11#(X1,active(X2)) -> U11#(X1,X2) U11#(X1,mark(X2)) -> U11#(X1,X2) -> U11#(active(X1),X2) -> U11#(X1,X2) U11#(X1,mark(X2)) -> U11#(X1,X2) -> U11#(X1,mark(X2)) -> U11#(X1,X2) U11#(X1,mark(X2)) -> U11#(X1,X2) -> U11#(mark(X1),X2) -> U11#(X1,X2) U11#(X1,active(X2)) -> U11#(X1,X2) -> U11#(X1,active(X2)) -> U11#(X1,X2) U11#(X1,active(X2)) -> U11#(X1,X2) -> U11#(active(X1),X2) -> U11#(X1,X2) U11#(X1,active(X2)) -> U11#(X1,X2) -> U11#(X1,mark(X2)) -> U11#(X1,X2) U11#(X1,active(X2)) -> U11#(X1,X2) -> U11#(mark(X1),X2) -> U11#(X1,X2) 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) isNat#(mark(X)) -> isNat#(X) -> isNat#(active(X)) -> isNat#(X) isNat#(mark(X)) -> isNat#(X) -> isNat#(mark(X)) -> isNat#(X) isNat#(active(X)) -> isNat#(X) -> isNat#(active(X)) -> isNat#(X) isNat#(active(X)) -> isNat#(X) -> isNat#(mark(X)) -> isNat#(X) 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#(isNat(X)) -> active#(isNat(X)) -> active#(plus(N,s(M))) -> mark#(U21(and(isNat(M),isNat(N)),M,N)) mark#(isNat(X)) -> active#(isNat(X)) -> active#(plus(N,s(M))) -> U21#(and(isNat(M),isNat(N)),M,N) mark#(isNat(X)) -> active#(isNat(X)) -> active#(plus(N,s(M))) -> and#(isNat(M),isNat(N)) mark#(isNat(X)) -> active#(isNat(X)) -> active#(plus(N,s(M))) -> isNat#(M) mark#(isNat(X)) -> active#(isNat(X)) -> active#(plus(N,s(M))) -> isNat#(N) mark#(isNat(X)) -> active#(isNat(X)) -> active#(plus(N,0())) -> mark#(U11(isNat(N),N)) mark#(isNat(X)) -> active#(isNat(X)) -> active#(plus(N,0())) -> U11#(isNat(N),N) mark#(isNat(X)) -> active#(isNat(X)) -> active#(plus(N,0())) -> isNat#(N) mark#(isNat(X)) -> active#(isNat(X)) -> active#(isNat(s(V1))) -> mark#(isNat(V1)) mark#(isNat(X)) -> active#(isNat(X)) -> active#(isNat(s(V1))) -> isNat#(V1) mark#(isNat(X)) -> active#(isNat(X)) -> active#(isNat(plus(V1,V2))) -> mark#(and(isNat(V1),isNat(V2))) mark#(isNat(X)) -> active#(isNat(X)) -> active#(isNat(plus(V1,V2))) -> and#(isNat(V1),isNat(V2)) mark#(isNat(X)) -> active#(isNat(X)) -> active#(isNat(plus(V1,V2))) -> isNat#(V1) mark#(isNat(X)) -> active#(isNat(X)) -> active#(isNat(plus(V1,V2))) -> isNat#(V2) mark#(isNat(X)) -> active#(isNat(X)) -> active#(isNat(0())) -> mark#(tt()) mark#(isNat(X)) -> active#(isNat(X)) -> active#(and(tt(),X)) -> mark#(X) mark#(isNat(X)) -> active#(isNat(X)) -> active#(U21(tt(),M,N)) -> mark#(s(plus(N,M))) mark#(isNat(X)) -> active#(isNat(X)) -> active#(U21(tt(),M,N)) -> s#(plus(N,M)) mark#(isNat(X)) -> active#(isNat(X)) -> active#(U21(tt(),M,N)) -> plus#(N,M) mark#(isNat(X)) -> active#(isNat(X)) -> active#(U11(tt(),N)) -> mark#(N) mark#(0()) -> active#(0()) -> active#(plus(N,s(M))) -> mark#(U21(and(isNat(M),isNat(N)),M,N)) mark#(0()) -> active#(0()) -> active#(plus(N,s(M))) -> U21#(and(isNat(M),isNat(N)),M,N) mark#(0()) -> active#(0()) -> active#(plus(N,s(M))) -> and#(isNat(M),isNat(N)) mark#(0()) -> active#(0()) -> active#(plus(N,s(M))) -> isNat#(M) mark#(0()) -> active#(0()) -> active#(plus(N,s(M))) -> isNat#(N) mark#(0()) -> active#(0()) -> active#(plus(N,0())) -> mark#(U11(isNat(N),N)) mark#(0()) -> active#(0()) -> active#(plus(N,0())) -> U11#(isNat(N),N) mark#(0()) -> active#(0()) -> active#(plus(N,0())) -> isNat#(N) mark#(0()) -> active#(0()) -> active#(isNat(s(V1))) -> mark#(isNat(V1)) mark#(0()) -> active#(0()) -> active#(isNat(s(V1))) -> isNat#(V1) mark#(0()) -> active#(0()) -> active#(isNat(plus(V1,V2))) -> mark#(and(isNat(V1),isNat(V2))) mark#(0()) -> active#(0()) -> active#(isNat(plus(V1,V2))) -> and#(isNat(V1),isNat(V2)) mark#(0()) -> active#(0()) -> active#(isNat(plus(V1,V2))) -> isNat#(V1) mark#(0()) -> active#(0()) -> active#(isNat(plus(V1,V2))) -> isNat#(V2) mark#(0()) -> active#(0()) -> active#(isNat(0())) -> mark#(tt()) mark#(0()) -> active#(0()) -> active#(and(tt(),X)) -> mark#(X) mark#(0()) -> active#(0()) -> active#(U21(tt(),M,N)) -> mark#(s(plus(N,M))) mark#(0()) -> active#(0()) -> active#(U21(tt(),M,N)) -> s#(plus(N,M)) mark#(0()) -> active#(0()) -> active#(U21(tt(),M,N)) -> plus#(N,M) mark#(0()) -> active#(0()) -> active#(U11(tt(),N)) -> mark#(N) 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#(0()) -> active#(0()) mark#(and(X1,X2)) -> mark#(X1) -> mark#(isNat(X)) -> active#(isNat(X)) 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)) -> 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#(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#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(tt()) -> active#(tt()) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> U11#(mark(X1),X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(plus(N,s(M))) -> mark#(U21(and(isNat(M),isNat(N)),M,N)) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(plus(N,s(M))) -> U21#(and(isNat(M),isNat(N)),M,N) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(plus(N,s(M))) -> and#(isNat(M),isNat(N)) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(plus(N,s(M))) -> isNat#(M) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(plus(N,s(M))) -> isNat#(N) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(plus(N,0())) -> mark#(U11(isNat(N),N)) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(plus(N,0())) -> U11#(isNat(N),N) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(plus(N,0())) -> isNat#(N) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(isNat(s(V1))) -> mark#(isNat(V1)) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(isNat(s(V1))) -> isNat#(V1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(isNat(plus(V1,V2))) -> mark#(and(isNat(V1),isNat(V2))) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(isNat(plus(V1,V2))) -> and#(isNat(V1),isNat(V2)) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(isNat(plus(V1,V2))) -> isNat#(V1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(isNat(plus(V1,V2))) -> isNat#(V2) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(isNat(0())) -> mark#(tt()) 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#(U21(tt(),M,N)) -> mark#(s(plus(N,M))) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(U21(tt(),M,N)) -> s#(plus(N,M)) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(U21(tt(),M,N)) -> plus#(N,M) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) -> active#(U11(tt(),N)) -> mark#(N) 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#(0()) -> active#(0()) mark#(s(X)) -> mark#(X) -> mark#(isNat(X)) -> active#(isNat(X)) 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)) -> 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#(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#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) mark#(s(X)) -> mark#(X) -> mark#(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3) mark#(s(X)) -> mark#(X) -> mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(tt()) -> active#(tt()) mark#(s(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) mark#(s(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> U11#(mark(X1),X2) mark#(s(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(s(X)) -> active#(s(mark(X))) -> active#(plus(N,s(M))) -> mark#(U21(and(isNat(M),isNat(N)),M,N)) mark#(s(X)) -> active#(s(mark(X))) -> active#(plus(N,s(M))) -> U21#(and(isNat(M),isNat(N)),M,N) mark#(s(X)) -> active#(s(mark(X))) -> active#(plus(N,s(M))) -> and#(isNat(M),isNat(N)) mark#(s(X)) -> active#(s(mark(X))) -> active#(plus(N,s(M))) -> isNat#(M) mark#(s(X)) -> active#(s(mark(X))) -> active#(plus(N,s(M))) -> isNat#(N) mark#(s(X)) -> active#(s(mark(X))) -> active#(plus(N,0())) -> mark#(U11(isNat(N),N)) mark#(s(X)) -> active#(s(mark(X))) -> active#(plus(N,0())) -> U11#(isNat(N),N) mark#(s(X)) -> active#(s(mark(X))) -> active#(plus(N,0())) -> isNat#(N) mark#(s(X)) -> active#(s(mark(X))) -> active#(isNat(s(V1))) -> mark#(isNat(V1)) mark#(s(X)) -> active#(s(mark(X))) -> active#(isNat(s(V1))) -> isNat#(V1) mark#(s(X)) -> active#(s(mark(X))) -> active#(isNat(plus(V1,V2))) -> mark#(and(isNat(V1),isNat(V2))) mark#(s(X)) -> active#(s(mark(X))) -> active#(isNat(plus(V1,V2))) -> and#(isNat(V1),isNat(V2)) mark#(s(X)) -> active#(s(mark(X))) -> active#(isNat(plus(V1,V2))) -> isNat#(V1) mark#(s(X)) -> active#(s(mark(X))) -> active#(isNat(plus(V1,V2))) -> isNat#(V2) mark#(s(X)) -> active#(s(mark(X))) -> active#(isNat(0())) -> mark#(tt()) mark#(s(X)) -> active#(s(mark(X))) -> active#(and(tt(),X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) -> active#(U21(tt(),M,N)) -> mark#(s(plus(N,M))) mark#(s(X)) -> active#(s(mark(X))) -> active#(U21(tt(),M,N)) -> s#(plus(N,M)) mark#(s(X)) -> active#(s(mark(X))) -> active#(U21(tt(),M,N)) -> plus#(N,M) mark#(s(X)) -> active#(s(mark(X))) -> active#(U11(tt(),N)) -> mark#(N) 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#(0()) -> active#(0()) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(isNat(X)) -> active#(isNat(X)) 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#(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#(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#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(tt()) -> active#(tt()) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U11(X1,X2)) -> U11#(mark(X1),X2) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(isNat(X)) -> active#(isNat(X)) 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)) -> 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#(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#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(tt()) -> active#(tt()) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> U11#(mark(X1),X2) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(plus(N,s(M))) -> mark#(U21(and(isNat(M),isNat(N)),M,N)) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(plus(N,s(M))) -> U21#(and(isNat(M),isNat(N)),M,N) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(plus(N,s(M))) -> and#(isNat(M),isNat(N)) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(plus(N,s(M))) -> isNat#(M) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(plus(N,s(M))) -> isNat#(N) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(plus(N,0())) -> mark#(U11(isNat(N),N)) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(plus(N,0())) -> U11#(isNat(N),N) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(plus(N,0())) -> isNat#(N) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(isNat(s(V1))) -> mark#(isNat(V1)) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(isNat(s(V1))) -> isNat#(V1) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(isNat(plus(V1,V2))) -> mark#(and(isNat(V1),isNat(V2))) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(isNat(plus(V1,V2))) -> and#(isNat(V1),isNat(V2)) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(isNat(plus(V1,V2))) -> isNat#(V1) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(isNat(plus(V1,V2))) -> isNat#(V2) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(isNat(0())) -> mark#(tt()) 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#(U21(tt(),M,N)) -> mark#(s(plus(N,M))) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(U21(tt(),M,N)) -> s#(plus(N,M)) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(U21(tt(),M,N)) -> plus#(N,M) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(U11(tt(),N)) -> mark#(N) mark#(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3) -> U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3) mark#(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3) -> U21#(X1,active(X2),X3) -> U21#(X1,X2,X3) mark#(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3) -> U21#(active(X1),X2,X3) -> U21#(X1,X2,X3) mark#(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3) -> U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3) mark#(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3) -> U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3) mark#(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3) -> U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(isNat(X)) -> active#(isNat(X)) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(s(X)) -> active#(s(mark(X))) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(s(X)) -> s#(mark(X)) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(tt()) -> active#(tt()) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2)) -> U11#(mark(X1),X2) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) -> active#(plus(N,s(M))) -> mark#(U21(and(isNat(M),isNat(N)),M,N)) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) -> active#(plus(N,s(M))) -> U21#(and(isNat(M),isNat(N)),M,N) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) -> active#(plus(N,s(M))) -> and#(isNat(M),isNat(N)) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) -> active#(plus(N,s(M))) -> isNat#(M) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) -> active#(plus(N,s(M))) -> isNat#(N) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) -> active#(plus(N,0())) -> mark#(U11(isNat(N),N)) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) -> active#(plus(N,0())) -> U11#(isNat(N),N) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) -> active#(plus(N,0())) -> isNat#(N) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) -> active#(isNat(s(V1))) -> mark#(isNat(V1)) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) -> active#(isNat(s(V1))) -> isNat#(V1) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) -> active#(isNat(plus(V1,V2))) -> mark#(and(isNat(V1),isNat(V2))) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) -> active#(isNat(plus(V1,V2))) -> and#(isNat(V1),isNat(V2)) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) -> active#(isNat(plus(V1,V2))) -> isNat#(V1) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) -> active#(isNat(plus(V1,V2))) -> isNat#(V2) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) -> active#(isNat(0())) -> mark#(tt()) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) -> active#(and(tt(),X)) -> mark#(X) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) -> active#(U21(tt(),M,N)) -> mark#(s(plus(N,M))) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) -> active#(U21(tt(),M,N)) -> s#(plus(N,M)) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) -> active#(U21(tt(),M,N)) -> plus#(N,M) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) -> active#(U11(tt(),N)) -> mark#(N) mark#(U11(X1,X2)) -> U11#(mark(X1),X2) -> U11#(X1,active(X2)) -> U11#(X1,X2) mark#(U11(X1,X2)) -> U11#(mark(X1),X2) -> U11#(active(X1),X2) -> U11#(X1,X2) mark#(U11(X1,X2)) -> U11#(mark(X1),X2) -> U11#(X1,mark(X2)) -> U11#(X1,X2) mark#(U11(X1,X2)) -> U11#(mark(X1),X2) -> U11#(mark(X1),X2) -> U11#(X1,X2) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(isNat(X)) -> active#(isNat(X)) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> active#(s(mark(X))) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> s#(mark(X)) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(tt()) -> active#(tt()) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> U11#(mark(X1),X2) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) -> active#(plus(N,s(M))) -> mark#(U21(and(isNat(M),isNat(N)),M,N)) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) -> active#(plus(N,s(M))) -> U21#(and(isNat(M),isNat(N)),M,N) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) -> active#(plus(N,s(M))) -> and#(isNat(M),isNat(N)) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) -> active#(plus(N,s(M))) -> isNat#(M) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) -> active#(plus(N,s(M))) -> isNat#(N) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) -> active#(plus(N,0())) -> mark#(U11(isNat(N),N)) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) -> active#(plus(N,0())) -> U11#(isNat(N),N) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) -> active#(plus(N,0())) -> isNat#(N) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) -> active#(isNat(s(V1))) -> mark#(isNat(V1)) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) -> active#(isNat(s(V1))) -> isNat#(V1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) -> active#(isNat(plus(V1,V2))) -> mark#(and(isNat(V1),isNat(V2))) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) -> active#(isNat(plus(V1,V2))) -> and#(isNat(V1),isNat(V2)) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) -> active#(isNat(plus(V1,V2))) -> isNat#(V1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) -> active#(isNat(plus(V1,V2))) -> isNat#(V2) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) -> active#(isNat(0())) -> mark#(tt()) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) -> active#(and(tt(),X)) -> mark#(X) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) -> active#(U21(tt(),M,N)) -> mark#(s(plus(N,M))) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) -> active#(U21(tt(),M,N)) -> s#(plus(N,M)) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) -> active#(U21(tt(),M,N)) -> plus#(N,M) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) -> active#(U11(tt(),N)) -> mark#(N) mark#(tt()) -> active#(tt()) -> active#(plus(N,s(M))) -> mark#(U21(and(isNat(M),isNat(N)),M,N)) mark#(tt()) -> active#(tt()) -> active#(plus(N,s(M))) -> U21#(and(isNat(M),isNat(N)),M,N) mark#(tt()) -> active#(tt()) -> active#(plus(N,s(M))) -> and#(isNat(M),isNat(N)) mark#(tt()) -> active#(tt()) -> active#(plus(N,s(M))) -> isNat#(M) mark#(tt()) -> active#(tt()) -> active#(plus(N,s(M))) -> isNat#(N) mark#(tt()) -> active#(tt()) -> active#(plus(N,0())) -> mark#(U11(isNat(N),N)) mark#(tt()) -> active#(tt()) -> active#(plus(N,0())) -> U11#(isNat(N),N) mark#(tt()) -> active#(tt()) -> active#(plus(N,0())) -> isNat#(N) mark#(tt()) -> active#(tt()) -> active#(isNat(s(V1))) -> mark#(isNat(V1)) mark#(tt()) -> active#(tt()) -> active#(isNat(s(V1))) -> isNat#(V1) mark#(tt()) -> active#(tt()) -> active#(isNat(plus(V1,V2))) -> mark#(and(isNat(V1),isNat(V2))) mark#(tt()) -> active#(tt()) -> active#(isNat(plus(V1,V2))) -> and#(isNat(V1),isNat(V2)) mark#(tt()) -> active#(tt()) -> active#(isNat(plus(V1,V2))) -> isNat#(V1) mark#(tt()) -> active#(tt()) -> active#(isNat(plus(V1,V2))) -> isNat#(V2) mark#(tt()) -> active#(tt()) -> active#(isNat(0())) -> mark#(tt()) mark#(tt()) -> active#(tt()) -> active#(and(tt(),X)) -> mark#(X) mark#(tt()) -> active#(tt()) -> active#(U21(tt(),M,N)) -> mark#(s(plus(N,M))) mark#(tt()) -> active#(tt()) -> active#(U21(tt(),M,N)) -> s#(plus(N,M)) mark#(tt()) -> active#(tt()) -> active#(U21(tt(),M,N)) -> plus#(N,M) mark#(tt()) -> active#(tt()) -> active#(U11(tt(),N)) -> mark#(N) active#(isNat(0())) -> mark#(tt()) -> mark#(0()) -> active#(0()) active#(isNat(0())) -> mark#(tt()) -> mark#(isNat(X)) -> active#(isNat(X)) active#(isNat(0())) -> mark#(tt()) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(isNat(0())) -> mark#(tt()) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) active#(isNat(0())) -> mark#(tt()) -> mark#(and(X1,X2)) -> mark#(X1) active#(isNat(0())) -> mark#(tt()) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(isNat(0())) -> mark#(tt()) -> mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) active#(isNat(0())) -> mark#(tt()) -> mark#(plus(X1,X2)) -> mark#(X1) active#(isNat(0())) -> mark#(tt()) -> mark#(plus(X1,X2)) -> mark#(X2) active#(isNat(0())) -> mark#(tt()) -> mark#(s(X)) -> active#(s(mark(X))) active#(isNat(0())) -> mark#(tt()) -> mark#(s(X)) -> s#(mark(X)) active#(isNat(0())) -> mark#(tt()) -> mark#(s(X)) -> mark#(X) active#(isNat(0())) -> mark#(tt()) -> mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) active#(isNat(0())) -> mark#(tt()) -> mark#(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3) active#(isNat(0())) -> mark#(tt()) -> mark#(U21(X1,X2,X3)) -> mark#(X1) active#(isNat(0())) -> mark#(tt()) -> mark#(tt()) -> active#(tt()) active#(isNat(0())) -> mark#(tt()) -> mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(isNat(0())) -> mark#(tt()) -> mark#(U11(X1,X2)) -> U11#(mark(X1),X2) active#(isNat(0())) -> mark#(tt()) -> mark#(U11(X1,X2)) -> mark#(X1) active#(isNat(s(V1))) -> isNat#(V1) -> isNat#(active(X)) -> isNat#(X) active#(isNat(s(V1))) -> isNat#(V1) -> isNat#(mark(X)) -> isNat#(X) active#(isNat(s(V1))) -> mark#(isNat(V1)) -> mark#(0()) -> active#(0()) active#(isNat(s(V1))) -> mark#(isNat(V1)) -> mark#(isNat(X)) -> active#(isNat(X)) active#(isNat(s(V1))) -> mark#(isNat(V1)) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(isNat(s(V1))) -> mark#(isNat(V1)) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) active#(isNat(s(V1))) -> mark#(isNat(V1)) -> mark#(and(X1,X2)) -> mark#(X1) active#(isNat(s(V1))) -> mark#(isNat(V1)) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(isNat(s(V1))) -> mark#(isNat(V1)) -> mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) active#(isNat(s(V1))) -> mark#(isNat(V1)) -> mark#(plus(X1,X2)) -> mark#(X1) active#(isNat(s(V1))) -> mark#(isNat(V1)) -> mark#(plus(X1,X2)) -> mark#(X2) active#(isNat(s(V1))) -> mark#(isNat(V1)) -> mark#(s(X)) -> active#(s(mark(X))) active#(isNat(s(V1))) -> mark#(isNat(V1)) -> mark#(s(X)) -> s#(mark(X)) active#(isNat(s(V1))) -> mark#(isNat(V1)) -> mark#(s(X)) -> mark#(X) active#(isNat(s(V1))) -> mark#(isNat(V1)) -> mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(isNat(V1)) -> mark#(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3) active#(isNat(s(V1))) -> mark#(isNat(V1)) -> mark#(U21(X1,X2,X3)) -> mark#(X1) active#(isNat(s(V1))) -> mark#(isNat(V1)) -> mark#(tt()) -> active#(tt()) active#(isNat(s(V1))) -> mark#(isNat(V1)) -> mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(isNat(s(V1))) -> mark#(isNat(V1)) -> mark#(U11(X1,X2)) -> U11#(mark(X1),X2) active#(isNat(s(V1))) -> mark#(isNat(V1)) -> mark#(U11(X1,X2)) -> mark#(X1) active#(isNat(plus(V1,V2))) -> and#(isNat(V1),isNat(V2)) -> and#(X1,active(X2)) -> and#(X1,X2) active#(isNat(plus(V1,V2))) -> and#(isNat(V1),isNat(V2)) -> and#(active(X1),X2) -> and#(X1,X2) active#(isNat(plus(V1,V2))) -> and#(isNat(V1),isNat(V2)) -> and#(X1,mark(X2)) -> and#(X1,X2) active#(isNat(plus(V1,V2))) -> and#(isNat(V1),isNat(V2)) -> and#(mark(X1),X2) -> and#(X1,X2) active#(isNat(plus(V1,V2))) -> isNat#(V2) -> isNat#(active(X)) -> isNat#(X) active#(isNat(plus(V1,V2))) -> isNat#(V2) -> isNat#(mark(X)) -> isNat#(X) active#(isNat(plus(V1,V2))) -> isNat#(V1) -> isNat#(active(X)) -> isNat#(X) active#(isNat(plus(V1,V2))) -> isNat#(V1) -> isNat#(mark(X)) -> isNat#(X) active#(isNat(plus(V1,V2))) -> mark#(and(isNat(V1),isNat(V2))) -> mark#(0()) -> active#(0()) active#(isNat(plus(V1,V2))) -> mark#(and(isNat(V1),isNat(V2))) -> mark#(isNat(X)) -> active#(isNat(X)) active#(isNat(plus(V1,V2))) -> mark#(and(isNat(V1),isNat(V2))) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(isNat(plus(V1,V2))) -> mark#(and(isNat(V1),isNat(V2))) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) active#(isNat(plus(V1,V2))) -> mark#(and(isNat(V1),isNat(V2))) -> mark#(and(X1,X2)) -> mark#(X1) active#(isNat(plus(V1,V2))) -> mark#(and(isNat(V1),isNat(V2))) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(isNat(plus(V1,V2))) -> mark#(and(isNat(V1),isNat(V2))) -> mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) active#(isNat(plus(V1,V2))) -> mark#(and(isNat(V1),isNat(V2))) -> mark#(plus(X1,X2)) -> mark#(X1) active#(isNat(plus(V1,V2))) -> mark#(and(isNat(V1),isNat(V2))) -> mark#(plus(X1,X2)) -> mark#(X2) active#(isNat(plus(V1,V2))) -> mark#(and(isNat(V1),isNat(V2))) -> mark#(s(X)) -> active#(s(mark(X))) active#(isNat(plus(V1,V2))) -> mark#(and(isNat(V1),isNat(V2))) -> mark#(s(X)) -> s#(mark(X)) active#(isNat(plus(V1,V2))) -> mark#(and(isNat(V1),isNat(V2))) -> mark#(s(X)) -> mark#(X) active#(isNat(plus(V1,V2))) -> mark#(and(isNat(V1),isNat(V2))) -> mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) active#(isNat(plus(V1,V2))) -> mark#(and(isNat(V1),isNat(V2))) -> mark#(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3) active#(isNat(plus(V1,V2))) -> mark#(and(isNat(V1),isNat(V2))) -> mark#(U21(X1,X2,X3)) -> mark#(X1) active#(isNat(plus(V1,V2))) -> mark#(and(isNat(V1),isNat(V2))) -> mark#(tt()) -> active#(tt()) active#(isNat(plus(V1,V2))) -> mark#(and(isNat(V1),isNat(V2))) -> mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(isNat(plus(V1,V2))) -> mark#(and(isNat(V1),isNat(V2))) -> mark#(U11(X1,X2)) -> U11#(mark(X1),X2) active#(isNat(plus(V1,V2))) -> mark#(and(isNat(V1),isNat(V2))) -> mark#(U11(X1,X2)) -> mark#(X1) active#(and(tt(),X)) -> mark#(X) -> mark#(0()) -> active#(0()) active#(and(tt(),X)) -> mark#(X) -> mark#(isNat(X)) -> active#(isNat(X)) 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) 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#(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#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) active#(and(tt(),X)) -> mark#(X) -> mark#(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3) active#(and(tt(),X)) -> mark#(X) -> mark#(U21(X1,X2,X3)) -> mark#(X1) active#(and(tt(),X)) -> mark#(X) -> mark#(tt()) -> active#(tt()) active#(and(tt(),X)) -> mark#(X) -> mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(and(tt(),X)) -> mark#(X) -> mark#(U11(X1,X2)) -> U11#(mark(X1),X2) active#(and(tt(),X)) -> mark#(X) -> mark#(U11(X1,X2)) -> mark#(X1) active#(plus(N,0())) -> U11#(isNat(N),N) -> U11#(X1,active(X2)) -> U11#(X1,X2) active#(plus(N,0())) -> U11#(isNat(N),N) -> U11#(active(X1),X2) -> U11#(X1,X2) active#(plus(N,0())) -> U11#(isNat(N),N) -> U11#(X1,mark(X2)) -> U11#(X1,X2) active#(plus(N,0())) -> U11#(isNat(N),N) -> U11#(mark(X1),X2) -> U11#(X1,X2) active#(plus(N,0())) -> isNat#(N) -> isNat#(active(X)) -> isNat#(X) active#(plus(N,0())) -> isNat#(N) -> isNat#(mark(X)) -> isNat#(X) active#(plus(N,0())) -> mark#(U11(isNat(N),N)) -> mark#(0()) -> active#(0()) active#(plus(N,0())) -> mark#(U11(isNat(N),N)) -> mark#(isNat(X)) -> active#(isNat(X)) active#(plus(N,0())) -> mark#(U11(isNat(N),N)) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(plus(N,0())) -> mark#(U11(isNat(N),N)) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) active#(plus(N,0())) -> mark#(U11(isNat(N),N)) -> mark#(and(X1,X2)) -> mark#(X1) active#(plus(N,0())) -> mark#(U11(isNat(N),N)) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(plus(N,0())) -> mark#(U11(isNat(N),N)) -> mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) active#(plus(N,0())) -> mark#(U11(isNat(N),N)) -> mark#(plus(X1,X2)) -> mark#(X1) active#(plus(N,0())) -> mark#(U11(isNat(N),N)) -> mark#(plus(X1,X2)) -> mark#(X2) active#(plus(N,0())) -> mark#(U11(isNat(N),N)) -> mark#(s(X)) -> active#(s(mark(X))) active#(plus(N,0())) -> mark#(U11(isNat(N),N)) -> mark#(s(X)) -> s#(mark(X)) active#(plus(N,0())) -> mark#(U11(isNat(N),N)) -> mark#(s(X)) -> mark#(X) active#(plus(N,0())) -> mark#(U11(isNat(N),N)) -> mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) active#(plus(N,0())) -> mark#(U11(isNat(N),N)) -> mark#(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3) active#(plus(N,0())) -> mark#(U11(isNat(N),N)) -> mark#(U21(X1,X2,X3)) -> mark#(X1) active#(plus(N,0())) -> mark#(U11(isNat(N),N)) -> mark#(tt()) -> active#(tt()) active#(plus(N,0())) -> mark#(U11(isNat(N),N)) -> mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(plus(N,0())) -> mark#(U11(isNat(N),N)) -> mark#(U11(X1,X2)) -> U11#(mark(X1),X2) active#(plus(N,0())) -> mark#(U11(isNat(N),N)) -> mark#(U11(X1,X2)) -> mark#(X1) active#(plus(N,s(M))) -> U21#(and(isNat(M),isNat(N)),M,N) -> U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3) active#(plus(N,s(M))) -> U21#(and(isNat(M),isNat(N)),M,N) -> U21#(X1,active(X2),X3) -> U21#(X1,X2,X3) active#(plus(N,s(M))) -> U21#(and(isNat(M),isNat(N)),M,N) -> U21#(active(X1),X2,X3) -> U21#(X1,X2,X3) active#(plus(N,s(M))) -> U21#(and(isNat(M),isNat(N)),M,N) -> U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3) active#(plus(N,s(M))) -> U21#(and(isNat(M),isNat(N)),M,N) -> U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3) active#(plus(N,s(M))) -> U21#(and(isNat(M),isNat(N)),M,N) -> U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) active#(plus(N,s(M))) -> and#(isNat(M),isNat(N)) -> and#(X1,active(X2)) -> and#(X1,X2) active#(plus(N,s(M))) -> and#(isNat(M),isNat(N)) -> and#(active(X1),X2) -> and#(X1,X2) active#(plus(N,s(M))) -> and#(isNat(M),isNat(N)) -> and#(X1,mark(X2)) -> and#(X1,X2) active#(plus(N,s(M))) -> and#(isNat(M),isNat(N)) -> and#(mark(X1),X2) -> and#(X1,X2) active#(plus(N,s(M))) -> isNat#(M) -> isNat#(active(X)) -> isNat#(X) active#(plus(N,s(M))) -> isNat#(M) -> isNat#(mark(X)) -> isNat#(X) active#(plus(N,s(M))) -> isNat#(N) -> isNat#(active(X)) -> isNat#(X) active#(plus(N,s(M))) -> isNat#(N) -> isNat#(mark(X)) -> isNat#(X) active#(plus(N,s(M))) -> mark#(U21(and(isNat(M),isNat(N)),M,N)) -> mark#(0()) -> active#(0()) active#(plus(N,s(M))) -> mark#(U21(and(isNat(M),isNat(N)),M,N)) -> mark#(isNat(X)) -> active#(isNat(X)) active#(plus(N,s(M))) -> mark#(U21(and(isNat(M),isNat(N)),M,N)) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(plus(N,s(M))) -> mark#(U21(and(isNat(M),isNat(N)),M,N)) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) active#(plus(N,s(M))) -> mark#(U21(and(isNat(M),isNat(N)),M,N)) -> mark#(and(X1,X2)) -> mark#(X1) active#(plus(N,s(M))) -> mark#(U21(and(isNat(M),isNat(N)),M,N)) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(plus(N,s(M))) -> mark#(U21(and(isNat(M),isNat(N)),M,N)) -> mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) active#(plus(N,s(M))) -> mark#(U21(and(isNat(M),isNat(N)),M,N)) -> mark#(plus(X1,X2)) -> mark#(X1) active#(plus(N,s(M))) -> mark#(U21(and(isNat(M),isNat(N)),M,N)) -> mark#(plus(X1,X2)) -> mark#(X2) active#(plus(N,s(M))) -> mark#(U21(and(isNat(M),isNat(N)),M,N)) -> mark#(s(X)) -> active#(s(mark(X))) active#(plus(N,s(M))) -> mark#(U21(and(isNat(M),isNat(N)),M,N)) -> mark#(s(X)) -> s#(mark(X)) active#(plus(N,s(M))) -> mark#(U21(and(isNat(M),isNat(N)),M,N)) -> mark#(s(X)) -> mark#(X) active#(plus(N,s(M))) -> mark#(U21(and(isNat(M),isNat(N)),M,N)) -> mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) active#(plus(N,s(M))) -> mark#(U21(and(isNat(M),isNat(N)),M,N)) -> mark#(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3) active#(plus(N,s(M))) -> mark#(U21(and(isNat(M),isNat(N)),M,N)) -> mark#(U21(X1,X2,X3)) -> mark#(X1) active#(plus(N,s(M))) -> mark#(U21(and(isNat(M),isNat(N)),M,N)) -> mark#(tt()) -> active#(tt()) active#(plus(N,s(M))) -> mark#(U21(and(isNat(M),isNat(N)),M,N)) -> mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(plus(N,s(M))) -> mark#(U21(and(isNat(M),isNat(N)),M,N)) -> mark#(U11(X1,X2)) -> U11#(mark(X1),X2) active#(plus(N,s(M))) -> mark#(U21(and(isNat(M),isNat(N)),M,N)) -> mark#(U11(X1,X2)) -> mark#(X1) active#(U21(tt(),M,N)) -> s#(plus(N,M)) -> s#(active(X)) -> s#(X) active#(U21(tt(),M,N)) -> s#(plus(N,M)) -> s#(mark(X)) -> s#(X) active#(U21(tt(),M,N)) -> plus#(N,M) -> plus#(X1,active(X2)) -> plus#(X1,X2) active#(U21(tt(),M,N)) -> plus#(N,M) -> plus#(active(X1),X2) -> plus#(X1,X2) active#(U21(tt(),M,N)) -> plus#(N,M) -> plus#(X1,mark(X2)) -> plus#(X1,X2) active#(U21(tt(),M,N)) -> plus#(N,M) -> plus#(mark(X1),X2) -> plus#(X1,X2) active#(U21(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(0()) -> active#(0()) active#(U21(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(isNat(X)) -> active#(isNat(X)) active#(U21(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(U21(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) active#(U21(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(and(X1,X2)) -> mark#(X1) active#(U21(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(U21(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) active#(U21(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(plus(X1,X2)) -> mark#(X1) active#(U21(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(plus(X1,X2)) -> mark#(X2) active#(U21(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(s(X)) -> active#(s(mark(X))) active#(U21(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(s(X)) -> s#(mark(X)) active#(U21(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(s(X)) -> mark#(X) active#(U21(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) active#(U21(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3) active#(U21(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(U21(X1,X2,X3)) -> mark#(X1) active#(U21(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(tt()) -> active#(tt()) active#(U21(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U21(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(U11(X1,X2)) -> U11#(mark(X1),X2) active#(U21(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(U11(X1,X2)) -> mark#(X1) active#(U11(tt(),N)) -> mark#(N) -> mark#(0()) -> active#(0()) active#(U11(tt(),N)) -> mark#(N) -> mark#(isNat(X)) -> active#(isNat(X)) active#(U11(tt(),N)) -> mark#(N) -> mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(U11(tt(),N)) -> mark#(N) -> mark#(and(X1,X2)) -> and#(mark(X1),X2) active#(U11(tt(),N)) -> mark#(N) -> mark#(and(X1,X2)) -> mark#(X1) active#(U11(tt(),N)) -> mark#(N) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(U11(tt(),N)) -> mark#(N) -> mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) active#(U11(tt(),N)) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X1) active#(U11(tt(),N)) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X2) active#(U11(tt(),N)) -> mark#(N) -> mark#(s(X)) -> active#(s(mark(X))) active#(U11(tt(),N)) -> mark#(N) -> mark#(s(X)) -> s#(mark(X)) active#(U11(tt(),N)) -> mark#(N) -> mark#(s(X)) -> mark#(X) active#(U11(tt(),N)) -> mark#(N) -> mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) active#(U11(tt(),N)) -> mark#(N) -> mark#(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3) active#(U11(tt(),N)) -> mark#(N) -> mark#(U21(X1,X2,X3)) -> mark#(X1) active#(U11(tt(),N)) -> mark#(N) -> mark#(tt()) -> active#(tt()) active#(U11(tt(),N)) -> mark#(N) -> mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U11(tt(),N)) -> mark#(N) -> mark#(U11(X1,X2)) -> U11#(mark(X1),X2) active#(U11(tt(),N)) -> mark#(N) -> mark#(U11(X1,X2)) -> mark#(X1) Restore Modifier: DPs: active#(U11(tt(),N)) -> mark#(N) active#(U21(tt(),M,N)) -> plus#(N,M) active#(U21(tt(),M,N)) -> s#(plus(N,M)) active#(U21(tt(),M,N)) -> mark#(s(plus(N,M))) active#(and(tt(),X)) -> mark#(X) active#(isNat(0())) -> mark#(tt()) active#(isNat(plus(V1,V2))) -> isNat#(V2) active#(isNat(plus(V1,V2))) -> isNat#(V1) active#(isNat(plus(V1,V2))) -> and#(isNat(V1),isNat(V2)) active#(isNat(plus(V1,V2))) -> mark#(and(isNat(V1),isNat(V2))) active#(isNat(s(V1))) -> isNat#(V1) active#(isNat(s(V1))) -> mark#(isNat(V1)) active#(plus(N,0())) -> isNat#(N) active#(plus(N,0())) -> U11#(isNat(N),N) active#(plus(N,0())) -> mark#(U11(isNat(N),N)) active#(plus(N,s(M))) -> isNat#(N) active#(plus(N,s(M))) -> isNat#(M) active#(plus(N,s(M))) -> and#(isNat(M),isNat(N)) active#(plus(N,s(M))) -> U21#(and(isNat(M),isNat(N)),M,N) active#(plus(N,s(M))) -> mark#(U21(and(isNat(M),isNat(N)),M,N)) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> U11#(mark(X1),X2) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) mark#(tt()) -> active#(tt()) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) mark#(s(X)) -> mark#(X) mark#(s(X)) -> s#(mark(X)) mark#(s(X)) -> active#(s(mark(X))) 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#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> and#(mark(X1),X2) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) mark#(isNat(X)) -> active#(isNat(X)) mark#(0()) -> active#(0()) U11#(mark(X1),X2) -> U11#(X1,X2) U11#(X1,mark(X2)) -> U11#(X1,X2) U11#(active(X1),X2) -> U11#(X1,X2) U11#(X1,active(X2)) -> U11#(X1,X2) U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3) U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3) U21#(active(X1),X2,X3) -> U21#(X1,X2,X3) U21#(X1,active(X2),X3) -> U21#(X1,X2,X3) U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) 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) 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) isNat#(mark(X)) -> isNat#(X) isNat#(active(X)) -> isNat#(X) TRS: active(U11(tt(),N)) -> mark(N) active(U21(tt(),M,N)) -> mark(s(plus(N,M))) active(and(tt(),X)) -> mark(X) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(and(isNat(V1),isNat(V2))) active(isNat(s(V1))) -> mark(isNat(V1)) active(plus(N,0())) -> mark(U11(isNat(N),N)) active(plus(N,s(M))) -> mark(U21(and(isNat(M),isNat(N)),M,N)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(0()) -> active(0()) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) SCC Processor: #sccs: 7 #rules: 44 #arcs: 574/3721 DPs: mark#(isNat(X)) -> active#(isNat(X)) active#(U11(tt(),N)) -> mark#(N) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U21(tt(),M,N)) -> mark#(s(plus(N,M))) mark#(tt()) -> active#(tt()) active#(and(tt(),X)) -> mark#(X) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3)) active#(isNat(0())) -> mark#(tt()) mark#(s(X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) active#(isNat(plus(V1,V2))) -> mark#(and(isNat(V1),isNat(V2))) mark#(plus(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(isNat(s(V1))) -> mark#(isNat(V1)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),X2)) active#(plus(N,0())) -> mark#(U11(isNat(N),N)) mark#(0()) -> active#(0()) active#(plus(N,s(M))) -> mark#(U21(and(isNat(M),isNat(N)),M,N)) TRS: active(U11(tt(),N)) -> mark(N) active(U21(tt(),M,N)) -> mark(s(plus(N,M))) active(and(tt(),X)) -> mark(X) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(and(isNat(V1),isNat(V2))) active(isNat(s(V1))) -> mark(isNat(V1)) active(plus(N,0())) -> mark(U11(isNat(N),N)) active(plus(N,s(M))) -> mark(U21(and(isNat(M),isNat(N)),M,N)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(0()) -> active(0()) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) Open 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(U11(tt(),N)) -> mark(N) active(U21(tt(),M,N)) -> mark(s(plus(N,M))) active(and(tt(),X)) -> mark(X) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(and(isNat(V1),isNat(V2))) active(isNat(s(V1))) -> mark(isNat(V1)) active(plus(N,0())) -> mark(U11(isNat(N),N)) active(plus(N,s(M))) -> mark(U21(and(isNat(M),isNat(N)),M,N)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(0()) -> active(0()) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) Open DPs: s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) TRS: active(U11(tt(),N)) -> mark(N) active(U21(tt(),M,N)) -> mark(s(plus(N,M))) active(and(tt(),X)) -> mark(X) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(and(isNat(V1),isNat(V2))) active(isNat(s(V1))) -> mark(isNat(V1)) active(plus(N,0())) -> mark(U11(isNat(N),N)) active(plus(N,s(M))) -> mark(U21(and(isNat(M),isNat(N)),M,N)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(0()) -> active(0()) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) Open DPs: isNat#(mark(X)) -> isNat#(X) isNat#(active(X)) -> isNat#(X) TRS: active(U11(tt(),N)) -> mark(N) active(U21(tt(),M,N)) -> mark(s(plus(N,M))) active(and(tt(),X)) -> mark(X) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(and(isNat(V1),isNat(V2))) active(isNat(s(V1))) -> mark(isNat(V1)) active(plus(N,0())) -> mark(U11(isNat(N),N)) active(plus(N,s(M))) -> mark(U21(and(isNat(M),isNat(N)),M,N)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(0()) -> active(0()) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) Open 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(U11(tt(),N)) -> mark(N) active(U21(tt(),M,N)) -> mark(s(plus(N,M))) active(and(tt(),X)) -> mark(X) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(and(isNat(V1),isNat(V2))) active(isNat(s(V1))) -> mark(isNat(V1)) active(plus(N,0())) -> mark(U11(isNat(N),N)) active(plus(N,s(M))) -> mark(U21(and(isNat(M),isNat(N)),M,N)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(0()) -> active(0()) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) Open DPs: U11#(mark(X1),X2) -> U11#(X1,X2) U11#(X1,mark(X2)) -> U11#(X1,X2) U11#(active(X1),X2) -> U11#(X1,X2) U11#(X1,active(X2)) -> U11#(X1,X2) TRS: active(U11(tt(),N)) -> mark(N) active(U21(tt(),M,N)) -> mark(s(plus(N,M))) active(and(tt(),X)) -> mark(X) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(and(isNat(V1),isNat(V2))) active(isNat(s(V1))) -> mark(isNat(V1)) active(plus(N,0())) -> mark(U11(isNat(N),N)) active(plus(N,s(M))) -> mark(U21(and(isNat(M),isNat(N)),M,N)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(0()) -> active(0()) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) Open DPs: U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3) U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3) U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3) U21#(active(X1),X2,X3) -> U21#(X1,X2,X3) U21#(X1,active(X2),X3) -> U21#(X1,X2,X3) U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3) TRS: active(U11(tt(),N)) -> mark(N) active(U21(tt(),M,N)) -> mark(s(plus(N,M))) active(and(tt(),X)) -> mark(X) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(and(isNat(V1),isNat(V2))) active(isNat(s(V1))) -> mark(isNat(V1)) active(plus(N,0())) -> mark(U11(isNat(N),N)) active(plus(N,s(M))) -> mark(U21(and(isNat(M),isNat(N)),M,N)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(and(X1,X2)) -> active(and(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(0()) -> active(0()) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U21(mark(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,mark(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,mark(X3)) -> U21(X1,X2,X3) U21(active(X1),X2,X3) -> U21(X1,X2,X3) U21(X1,active(X2),X3) -> U21(X1,X2,X3) U21(X1,X2,active(X3)) -> U21(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) Open