MAYBE Problem: active(U11(tt(),V2)) -> mark(U12(isNat(V2))) active(U12(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt(),N)) -> mark(N) active(U41(tt(),M,N)) -> mark(U42(isNat(N),M,N)) active(U42(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNat(V1),V2)) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(plus(N,0())) -> mark(U31(isNat(N),N)) active(plus(N,s(M))) -> mark(U41(isNat(M),M,N)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) 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) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(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) Proof: DP Processor: DPs: active#(U11(tt(),V2)) -> isNat#(V2) active#(U11(tt(),V2)) -> U12#(isNat(V2)) active#(U11(tt(),V2)) -> mark#(U12(isNat(V2))) active#(U12(tt())) -> mark#(tt()) active#(U21(tt())) -> mark#(tt()) active#(U31(tt(),N)) -> mark#(N) active#(U41(tt(),M,N)) -> isNat#(N) active#(U41(tt(),M,N)) -> U42#(isNat(N),M,N) active#(U41(tt(),M,N)) -> mark#(U42(isNat(N),M,N)) active#(U42(tt(),M,N)) -> plus#(N,M) active#(U42(tt(),M,N)) -> s#(plus(N,M)) active#(U42(tt(),M,N)) -> mark#(s(plus(N,M))) active#(isNat(0())) -> mark#(tt()) active#(isNat(plus(V1,V2))) -> isNat#(V1) active#(isNat(plus(V1,V2))) -> U11#(isNat(V1),V2) active#(isNat(plus(V1,V2))) -> mark#(U11(isNat(V1),V2)) active#(isNat(s(V1))) -> isNat#(V1) active#(isNat(s(V1))) -> U21#(isNat(V1)) active#(isNat(s(V1))) -> mark#(U21(isNat(V1))) active#(plus(N,0())) -> isNat#(N) active#(plus(N,0())) -> U31#(isNat(N),N) active#(plus(N,0())) -> mark#(U31(isNat(N),N)) active#(plus(N,s(M))) -> isNat#(M) active#(plus(N,s(M))) -> U41#(isNat(M),M,N) active#(plus(N,s(M))) -> mark#(U41(isNat(M),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#(U12(X)) -> mark#(X) mark#(U12(X)) -> U12#(mark(X)) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNat(X)) -> active#(isNat(X)) mark#(U21(X)) -> mark#(X) mark#(U21(X)) -> U21#(mark(X)) mark#(U21(X)) -> active#(U21(mark(X))) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> U31#(mark(X1),X2) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> U41#(mark(X1),X2,X3) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> U42#(mark(X1),X2,X3) mark#(U42(X1,X2,X3)) -> active#(U42(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#(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) U12#(mark(X)) -> U12#(X) U12#(active(X)) -> U12#(X) isNat#(mark(X)) -> isNat#(X) isNat#(active(X)) -> isNat#(X) U21#(mark(X)) -> U21#(X) U21#(active(X)) -> U21#(X) U31#(mark(X1),X2) -> U31#(X1,X2) U31#(X1,mark(X2)) -> U31#(X1,X2) U31#(active(X1),X2) -> U31#(X1,X2) U31#(X1,active(X2)) -> U31#(X1,X2) U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3) U41#(X1,mark(X2),X3) -> U41#(X1,X2,X3) U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3) U41#(active(X1),X2,X3) -> U41#(X1,X2,X3) U41#(X1,active(X2),X3) -> U41#(X1,X2,X3) U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3) U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3) U42#(X1,mark(X2),X3) -> U42#(X1,X2,X3) U42#(X1,X2,mark(X3)) -> U42#(X1,X2,X3) U42#(active(X1),X2,X3) -> U42#(X1,X2,X3) U42#(X1,active(X2),X3) -> U42#(X1,X2,X3) U42#(X1,X2,active(X3)) -> U42#(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) TRS: active(U11(tt(),V2)) -> mark(U12(isNat(V2))) active(U12(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt(),N)) -> mark(N) active(U41(tt(),M,N)) -> mark(U42(isNat(N),M,N)) active(U42(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNat(V1),V2)) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(plus(N,0())) -> mark(U31(isNat(N),N)) active(plus(N,s(M))) -> mark(U41(isNat(M),M,N)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) 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) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(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) TDG Processor: DPs: active#(U11(tt(),V2)) -> isNat#(V2) active#(U11(tt(),V2)) -> U12#(isNat(V2)) active#(U11(tt(),V2)) -> mark#(U12(isNat(V2))) active#(U12(tt())) -> mark#(tt()) active#(U21(tt())) -> mark#(tt()) active#(U31(tt(),N)) -> mark#(N) active#(U41(tt(),M,N)) -> isNat#(N) active#(U41(tt(),M,N)) -> U42#(isNat(N),M,N) active#(U41(tt(),M,N)) -> mark#(U42(isNat(N),M,N)) active#(U42(tt(),M,N)) -> plus#(N,M) active#(U42(tt(),M,N)) -> s#(plus(N,M)) active#(U42(tt(),M,N)) -> mark#(s(plus(N,M))) active#(isNat(0())) -> mark#(tt()) active#(isNat(plus(V1,V2))) -> isNat#(V1) active#(isNat(plus(V1,V2))) -> U11#(isNat(V1),V2) active#(isNat(plus(V1,V2))) -> mark#(U11(isNat(V1),V2)) active#(isNat(s(V1))) -> isNat#(V1) active#(isNat(s(V1))) -> U21#(isNat(V1)) active#(isNat(s(V1))) -> mark#(U21(isNat(V1))) active#(plus(N,0())) -> isNat#(N) active#(plus(N,0())) -> U31#(isNat(N),N) active#(plus(N,0())) -> mark#(U31(isNat(N),N)) active#(plus(N,s(M))) -> isNat#(M) active#(plus(N,s(M))) -> U41#(isNat(M),M,N) active#(plus(N,s(M))) -> mark#(U41(isNat(M),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#(U12(X)) -> mark#(X) mark#(U12(X)) -> U12#(mark(X)) mark#(U12(X)) -> active#(U12(mark(X))) mark#(isNat(X)) -> active#(isNat(X)) mark#(U21(X)) -> mark#(X) mark#(U21(X)) -> U21#(mark(X)) mark#(U21(X)) -> active#(U21(mark(X))) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> U31#(mark(X1),X2) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> U41#(mark(X1),X2,X3) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> U42#(mark(X1),X2,X3) mark#(U42(X1,X2,X3)) -> active#(U42(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#(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) U12#(mark(X)) -> U12#(X) U12#(active(X)) -> U12#(X) isNat#(mark(X)) -> isNat#(X) isNat#(active(X)) -> isNat#(X) U21#(mark(X)) -> U21#(X) U21#(active(X)) -> U21#(X) U31#(mark(X1),X2) -> U31#(X1,X2) U31#(X1,mark(X2)) -> U31#(X1,X2) U31#(active(X1),X2) -> U31#(X1,X2) U31#(X1,active(X2)) -> U31#(X1,X2) U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3) U41#(X1,mark(X2),X3) -> U41#(X1,X2,X3) U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3) U41#(active(X1),X2,X3) -> U41#(X1,X2,X3) U41#(X1,active(X2),X3) -> U41#(X1,X2,X3) U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3) U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3) U42#(X1,mark(X2),X3) -> U42#(X1,X2,X3) U42#(X1,X2,mark(X3)) -> U42#(X1,X2,X3) U42#(active(X1),X2,X3) -> U42#(X1,X2,X3) U42#(X1,active(X2),X3) -> U42#(X1,X2,X3) U42#(X1,X2,active(X3)) -> U42#(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) TRS: active(U11(tt(),V2)) -> mark(U12(isNat(V2))) active(U12(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt(),N)) -> mark(N) active(U41(tt(),M,N)) -> mark(U42(isNat(N),M,N)) active(U42(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNat(V1),V2)) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(plus(N,0())) -> mark(U31(isNat(N),N)) active(plus(N,s(M))) -> mark(U41(isNat(M),M,N)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) 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) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(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) graph: ... SCC Processor: #sccs: 10 #rules: 63 #arcs: 1043/7225 DPs: mark#(0()) -> active#(0()) active#(U11(tt(),V2)) -> mark#(U12(isNat(V2))) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U12(tt())) -> mark#(tt()) mark#(tt()) -> active#(tt()) active#(U21(tt())) -> mark#(tt()) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> active#(U12(mark(X))) active#(U31(tt(),N)) -> mark#(N) mark#(isNat(X)) -> active#(isNat(X)) active#(U41(tt(),M,N)) -> mark#(U42(isNat(N),M,N)) mark#(U21(X)) -> mark#(X) mark#(U21(X)) -> active#(U21(mark(X))) active#(U42(tt(),M,N)) -> mark#(s(plus(N,M))) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(isNat(0())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(isNat(plus(V1,V2))) -> mark#(U11(isNat(V1),V2)) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNat(V1))) mark#(s(X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) active#(plus(N,0())) -> mark#(U31(isNat(N),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#(U41(isNat(M),M,N)) TRS: active(U11(tt(),V2)) -> mark(U12(isNat(V2))) active(U12(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt(),N)) -> mark(N) active(U41(tt(),M,N)) -> mark(U42(isNat(N),M,N)) active(U42(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNat(V1),V2)) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(plus(N,0())) -> mark(U31(isNat(N),N)) active(plus(N,s(M))) -> mark(U41(isNat(M),M,N)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) 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) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(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) Open DPs: U12#(mark(X)) -> U12#(X) U12#(active(X)) -> U12#(X) TRS: active(U11(tt(),V2)) -> mark(U12(isNat(V2))) active(U12(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt(),N)) -> mark(N) active(U41(tt(),M,N)) -> mark(U42(isNat(N),M,N)) active(U42(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNat(V1),V2)) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(plus(N,0())) -> mark(U31(isNat(N),N)) active(plus(N,s(M))) -> mark(U41(isNat(M),M,N)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) 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) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(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) Open DPs: isNat#(mark(X)) -> isNat#(X) isNat#(active(X)) -> isNat#(X) TRS: active(U11(tt(),V2)) -> mark(U12(isNat(V2))) active(U12(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt(),N)) -> mark(N) active(U41(tt(),M,N)) -> mark(U42(isNat(N),M,N)) active(U42(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNat(V1),V2)) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(plus(N,0())) -> mark(U31(isNat(N),N)) active(plus(N,s(M))) -> mark(U41(isNat(M),M,N)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) 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) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(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) Open DPs: U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3) U42#(X1,mark(X2),X3) -> U42#(X1,X2,X3) U42#(X1,X2,mark(X3)) -> U42#(X1,X2,X3) U42#(active(X1),X2,X3) -> U42#(X1,X2,X3) U42#(X1,active(X2),X3) -> U42#(X1,X2,X3) U42#(X1,X2,active(X3)) -> U42#(X1,X2,X3) TRS: active(U11(tt(),V2)) -> mark(U12(isNat(V2))) active(U12(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt(),N)) -> mark(N) active(U41(tt(),M,N)) -> mark(U42(isNat(N),M,N)) active(U42(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNat(V1),V2)) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(plus(N,0())) -> mark(U31(isNat(N),N)) active(plus(N,s(M))) -> mark(U41(isNat(M),M,N)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) 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) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(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) 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(),V2)) -> mark(U12(isNat(V2))) active(U12(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt(),N)) -> mark(N) active(U41(tt(),M,N)) -> mark(U42(isNat(N),M,N)) active(U42(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNat(V1),V2)) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(plus(N,0())) -> mark(U31(isNat(N),N)) active(plus(N,s(M))) -> mark(U41(isNat(M),M,N)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) 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) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(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) Open DPs: s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) TRS: active(U11(tt(),V2)) -> mark(U12(isNat(V2))) active(U12(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt(),N)) -> mark(N) active(U41(tt(),M,N)) -> mark(U42(isNat(N),M,N)) active(U42(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNat(V1),V2)) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(plus(N,0())) -> mark(U31(isNat(N),N)) active(plus(N,s(M))) -> mark(U41(isNat(M),M,N)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) 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) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(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) 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(),V2)) -> mark(U12(isNat(V2))) active(U12(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt(),N)) -> mark(N) active(U41(tt(),M,N)) -> mark(U42(isNat(N),M,N)) active(U42(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNat(V1),V2)) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(plus(N,0())) -> mark(U31(isNat(N),N)) active(plus(N,s(M))) -> mark(U41(isNat(M),M,N)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) 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) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(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) Open DPs: U21#(mark(X)) -> U21#(X) U21#(active(X)) -> U21#(X) TRS: active(U11(tt(),V2)) -> mark(U12(isNat(V2))) active(U12(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt(),N)) -> mark(N) active(U41(tt(),M,N)) -> mark(U42(isNat(N),M,N)) active(U42(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNat(V1),V2)) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(plus(N,0())) -> mark(U31(isNat(N),N)) active(plus(N,s(M))) -> mark(U41(isNat(M),M,N)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) 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) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(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) Open DPs: U31#(mark(X1),X2) -> U31#(X1,X2) U31#(X1,mark(X2)) -> U31#(X1,X2) U31#(active(X1),X2) -> U31#(X1,X2) U31#(X1,active(X2)) -> U31#(X1,X2) TRS: active(U11(tt(),V2)) -> mark(U12(isNat(V2))) active(U12(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt(),N)) -> mark(N) active(U41(tt(),M,N)) -> mark(U42(isNat(N),M,N)) active(U42(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNat(V1),V2)) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(plus(N,0())) -> mark(U31(isNat(N),N)) active(plus(N,s(M))) -> mark(U41(isNat(M),M,N)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) 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) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(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) Open DPs: U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3) U41#(X1,mark(X2),X3) -> U41#(X1,X2,X3) U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3) U41#(active(X1),X2,X3) -> U41#(X1,X2,X3) U41#(X1,active(X2),X3) -> U41#(X1,X2,X3) U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3) TRS: active(U11(tt(),V2)) -> mark(U12(isNat(V2))) active(U12(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt(),N)) -> mark(N) active(U41(tt(),M,N)) -> mark(U42(isNat(N),M,N)) active(U42(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNat(V1),V2)) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(plus(N,0())) -> mark(U31(isNat(N),N)) active(plus(N,s(M))) -> mark(U41(isNat(M),M,N)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) mark(isNat(X)) -> active(isNat(X)) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) 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) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(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) Open