MAYBE Problem: a__U11(tt(),M,N) -> a__U12(tt(),M,N) a__U12(tt(),M,N) -> s(a__plus(mark(N),mark(M))) a__U21(tt(),M,N) -> a__U22(tt(),M,N) a__U22(tt(),M,N) -> a__plus(a__x(mark(N),mark(M)),mark(N)) a__plus(N,0()) -> mark(N) a__plus(N,s(M)) -> a__U11(tt(),M,N) a__x(N,0()) -> 0() a__x(N,s(M)) -> a__U21(tt(),M,N) mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3) mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3) mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(x(X1,X2)) -> a__x(mark(X1),mark(X2)) mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(0()) -> 0() a__U11(X1,X2,X3) -> U11(X1,X2,X3) a__U12(X1,X2,X3) -> U12(X1,X2,X3) a__plus(X1,X2) -> plus(X1,X2) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__x(X1,X2) -> x(X1,X2) Proof: DP Processor: DPs: a__U11#(tt(),M,N) -> a__U12#(tt(),M,N) a__U12#(tt(),M,N) -> mark#(M) a__U12#(tt(),M,N) -> mark#(N) a__U12#(tt(),M,N) -> a__plus#(mark(N),mark(M)) a__U21#(tt(),M,N) -> a__U22#(tt(),M,N) a__U22#(tt(),M,N) -> mark#(M) a__U22#(tt(),M,N) -> mark#(N) a__U22#(tt(),M,N) -> a__x#(mark(N),mark(M)) a__U22#(tt(),M,N) -> a__plus#(a__x(mark(N),mark(M)),mark(N)) a__plus#(N,0()) -> mark#(N) a__plus#(N,s(M)) -> a__U11#(tt(),M,N) a__x#(N,s(M)) -> a__U21#(tt(),M,N) mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) mark#(plus(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) mark#(x(X1,X2)) -> mark#(X2) mark#(x(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) mark#(s(X)) -> mark#(X) TRS: a__U11(tt(),M,N) -> a__U12(tt(),M,N) a__U12(tt(),M,N) -> s(a__plus(mark(N),mark(M))) a__U21(tt(),M,N) -> a__U22(tt(),M,N) a__U22(tt(),M,N) -> a__plus(a__x(mark(N),mark(M)),mark(N)) a__plus(N,0()) -> mark(N) a__plus(N,s(M)) -> a__U11(tt(),M,N) a__x(N,0()) -> 0() a__x(N,s(M)) -> a__U21(tt(),M,N) mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3) mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3) mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(x(X1,X2)) -> a__x(mark(X1),mark(X2)) mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(0()) -> 0() a__U11(X1,X2,X3) -> U11(X1,X2,X3) a__U12(X1,X2,X3) -> U12(X1,X2,X3) a__plus(X1,X2) -> plus(X1,X2) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__x(X1,X2) -> x(X1,X2) TDG Processor: DPs: a__U11#(tt(),M,N) -> a__U12#(tt(),M,N) a__U12#(tt(),M,N) -> mark#(M) a__U12#(tt(),M,N) -> mark#(N) a__U12#(tt(),M,N) -> a__plus#(mark(N),mark(M)) a__U21#(tt(),M,N) -> a__U22#(tt(),M,N) a__U22#(tt(),M,N) -> mark#(M) a__U22#(tt(),M,N) -> mark#(N) a__U22#(tt(),M,N) -> a__x#(mark(N),mark(M)) a__U22#(tt(),M,N) -> a__plus#(a__x(mark(N),mark(M)),mark(N)) a__plus#(N,0()) -> mark#(N) a__plus#(N,s(M)) -> a__U11#(tt(),M,N) a__x#(N,s(M)) -> a__U21#(tt(),M,N) mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) mark#(plus(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) mark#(x(X1,X2)) -> mark#(X2) mark#(x(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) mark#(s(X)) -> mark#(X) TRS: a__U11(tt(),M,N) -> a__U12(tt(),M,N) a__U12(tt(),M,N) -> s(a__plus(mark(N),mark(M))) a__U21(tt(),M,N) -> a__U22(tt(),M,N) a__U22(tt(),M,N) -> a__plus(a__x(mark(N),mark(M)),mark(N)) a__plus(N,0()) -> mark(N) a__plus(N,s(M)) -> a__U11(tt(),M,N) a__x(N,0()) -> 0() a__x(N,s(M)) -> a__U21(tt(),M,N) mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3) mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3) mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(x(X1,X2)) -> a__x(mark(X1),mark(X2)) mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(0()) -> 0() a__U11(X1,X2,X3) -> U11(X1,X2,X3) a__U12(X1,X2,X3) -> U12(X1,X2,X3) a__plus(X1,X2) -> plus(X1,X2) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__x(X1,X2) -> x(X1,X2) graph: a__x#(N,s(M)) -> a__U21#(tt(),M,N) -> a__U21#(tt(),M,N) -> a__U22#(tt(),M,N) a__U22#(tt(),M,N) -> a__x#(mark(N),mark(M)) -> a__x#(N,s(M)) -> a__U21#(tt(),M,N) a__U22#(tt(),M,N) -> a__plus#(a__x(mark(N),mark(M)),mark(N)) -> a__plus#(N,s(M)) -> a__U11#(tt(),M,N) a__U22#(tt(),M,N) -> a__plus#(a__x(mark(N),mark(M)),mark(N)) -> a__plus#(N,0()) -> mark#(N) a__U22#(tt(),M,N) -> mark#(N) -> mark#(s(X)) -> mark#(X) a__U22#(tt(),M,N) -> mark#(N) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) a__U22#(tt(),M,N) -> mark#(N) -> mark#(x(X1,X2)) -> mark#(X1) a__U22#(tt(),M,N) -> mark#(N) -> mark#(x(X1,X2)) -> mark#(X2) a__U22#(tt(),M,N) -> mark#(N) -> mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) a__U22#(tt(),M,N) -> mark#(N) -> mark#(U22(X1,X2,X3)) -> mark#(X1) a__U22#(tt(),M,N) -> mark#(N) -> mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) a__U22#(tt(),M,N) -> mark#(N) -> mark#(U21(X1,X2,X3)) -> mark#(X1) a__U22#(tt(),M,N) -> mark#(N) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) a__U22#(tt(),M,N) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X1) a__U22#(tt(),M,N) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X2) a__U22#(tt(),M,N) -> mark#(N) -> mark#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) a__U22#(tt(),M,N) -> mark#(N) -> mark#(U12(X1,X2,X3)) -> mark#(X1) a__U22#(tt(),M,N) -> mark#(N) -> mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) a__U22#(tt(),M,N) -> mark#(N) -> mark#(U11(X1,X2,X3)) -> mark#(X1) a__U22#(tt(),M,N) -> mark#(M) -> mark#(s(X)) -> mark#(X) a__U22#(tt(),M,N) -> mark#(M) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) a__U22#(tt(),M,N) -> mark#(M) -> mark#(x(X1,X2)) -> mark#(X1) a__U22#(tt(),M,N) -> mark#(M) -> mark#(x(X1,X2)) -> mark#(X2) a__U22#(tt(),M,N) -> mark#(M) -> mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) a__U22#(tt(),M,N) -> mark#(M) -> mark#(U22(X1,X2,X3)) -> mark#(X1) a__U22#(tt(),M,N) -> mark#(M) -> mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) a__U22#(tt(),M,N) -> mark#(M) -> mark#(U21(X1,X2,X3)) -> mark#(X1) a__U22#(tt(),M,N) -> mark#(M) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) a__U22#(tt(),M,N) -> mark#(M) -> mark#(plus(X1,X2)) -> mark#(X1) a__U22#(tt(),M,N) -> mark#(M) -> mark#(plus(X1,X2)) -> mark#(X2) a__U22#(tt(),M,N) -> mark#(M) -> mark#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) a__U22#(tt(),M,N) -> mark#(M) -> mark#(U12(X1,X2,X3)) -> mark#(X1) a__U22#(tt(),M,N) -> mark#(M) -> mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) a__U22#(tt(),M,N) -> mark#(M) -> mark#(U11(X1,X2,X3)) -> mark#(X1) a__U21#(tt(),M,N) -> a__U22#(tt(),M,N) -> a__U22#(tt(),M,N) -> a__plus#(a__x(mark(N),mark(M)),mark(N)) a__U21#(tt(),M,N) -> a__U22#(tt(),M,N) -> a__U22#(tt(),M,N) -> a__x#(mark(N),mark(M)) a__U21#(tt(),M,N) -> a__U22#(tt(),M,N) -> a__U22#(tt(),M,N) -> mark#(N) a__U21#(tt(),M,N) -> a__U22#(tt(),M,N) -> a__U22#(tt(),M,N) -> mark#(M) a__plus#(N,0()) -> mark#(N) -> mark#(s(X)) -> mark#(X) a__plus#(N,0()) -> mark#(N) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) a__plus#(N,0()) -> mark#(N) -> mark#(x(X1,X2)) -> mark#(X1) a__plus#(N,0()) -> mark#(N) -> mark#(x(X1,X2)) -> mark#(X2) a__plus#(N,0()) -> mark#(N) -> mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) a__plus#(N,0()) -> mark#(N) -> mark#(U22(X1,X2,X3)) -> mark#(X1) a__plus#(N,0()) -> mark#(N) -> mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) a__plus#(N,0()) -> mark#(N) -> mark#(U21(X1,X2,X3)) -> mark#(X1) a__plus#(N,0()) -> mark#(N) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) a__plus#(N,0()) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X1) a__plus#(N,0()) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X2) a__plus#(N,0()) -> mark#(N) -> mark#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) a__plus#(N,0()) -> mark#(N) -> mark#(U12(X1,X2,X3)) -> mark#(X1) a__plus#(N,0()) -> mark#(N) -> mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) a__plus#(N,0()) -> mark#(N) -> mark#(U11(X1,X2,X3)) -> mark#(X1) a__plus#(N,s(M)) -> a__U11#(tt(),M,N) -> a__U11#(tt(),M,N) -> a__U12#(tt(),M,N) mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) -> a__x#(N,s(M)) -> a__U21#(tt(),M,N) mark#(x(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X) mark#(x(X1,X2)) -> mark#(X2) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) mark#(x(X1,X2)) -> mark#(X2) -> mark#(x(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X2) -> mark#(x(X1,X2)) -> mark#(X2) mark#(x(X1,X2)) -> mark#(X2) -> mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) mark#(x(X1,X2)) -> mark#(X2) -> mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X2) -> mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) mark#(x(X1,X2)) -> mark#(X2) -> mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X2) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) mark#(x(X1,X2)) -> mark#(X2) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X2) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(x(X1,X2)) -> mark#(X2) -> mark#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) mark#(x(X1,X2)) -> mark#(X2) -> mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X2) -> mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) mark#(x(X1,X2)) -> mark#(X2) -> mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(x(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) mark#(x(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X2) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) mark#(x(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) mark#(x(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) -> a__U22#(tt(),M,N) -> a__plus#(a__x(mark(N),mark(M)),mark(N)) mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) -> a__U22#(tt(),M,N) -> a__x#(mark(N),mark(M)) mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) -> a__U22#(tt(),M,N) -> mark#(N) mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) -> a__U22#(tt(),M,N) -> mark#(M) mark#(U22(X1,X2,X3)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U22(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) mark#(U22(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X1) mark#(U22(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X2) mark#(U22(X1,X2,X3)) -> mark#(X1) -> mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) mark#(U22(X1,X2,X3)) -> mark#(X1) -> mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(U22(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) mark#(U22(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U22(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) mark#(U22(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(U22(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(U22(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) mark#(U22(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(U22(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) mark#(U22(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) -> a__U21#(tt(),M,N) -> a__U22#(tt(),M,N) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X2) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X1,X2,X3)) -> a__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#(plus(X1,X2)) -> a__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#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) mark#(U21(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) -> a__plus#(N,s(M)) -> a__U11#(tt(),M,N) mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) -> a__plus#(N,0()) -> mark#(N) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(x(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(x(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U21(X1,X2,X3)) -> a__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#(plus(X1,X2)) -> a__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#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2,X3)) -> a__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#(plus(X1,X2)) -> a__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#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X1) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X2) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) -> a__U12#(tt(),M,N) -> a__plus#(mark(N),mark(M)) mark#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) -> a__U12#(tt(),M,N) -> mark#(N) mark#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) -> a__U12#(tt(),M,N) -> mark#(M) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X1) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X2) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) -> a__U11#(tt(),M,N) -> a__U12#(tt(),M,N) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) mark#(s(X)) -> mark#(X) -> mark#(x(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(x(X1,X2)) -> mark#(X2) mark#(s(X)) -> mark#(X) -> mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) mark#(s(X)) -> mark#(X) -> mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) mark#(s(X)) -> mark#(X) -> mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(plus(X1,X2)) -> a__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#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) mark#(s(X)) -> mark#(X) -> mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) mark#(s(X)) -> mark#(X) -> mark#(U11(X1,X2,X3)) -> mark#(X1) a__U12#(tt(),M,N) -> a__plus#(mark(N),mark(M)) -> a__plus#(N,s(M)) -> a__U11#(tt(),M,N) a__U12#(tt(),M,N) -> a__plus#(mark(N),mark(M)) -> a__plus#(N,0()) -> mark#(N) a__U12#(tt(),M,N) -> mark#(N) -> mark#(s(X)) -> mark#(X) a__U12#(tt(),M,N) -> mark#(N) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) a__U12#(tt(),M,N) -> mark#(N) -> mark#(x(X1,X2)) -> mark#(X1) a__U12#(tt(),M,N) -> mark#(N) -> mark#(x(X1,X2)) -> mark#(X2) a__U12#(tt(),M,N) -> mark#(N) -> mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) a__U12#(tt(),M,N) -> mark#(N) -> mark#(U22(X1,X2,X3)) -> mark#(X1) a__U12#(tt(),M,N) -> mark#(N) -> mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) a__U12#(tt(),M,N) -> mark#(N) -> mark#(U21(X1,X2,X3)) -> mark#(X1) a__U12#(tt(),M,N) -> mark#(N) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) a__U12#(tt(),M,N) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X1) a__U12#(tt(),M,N) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X2) a__U12#(tt(),M,N) -> mark#(N) -> mark#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) a__U12#(tt(),M,N) -> mark#(N) -> mark#(U12(X1,X2,X3)) -> mark#(X1) a__U12#(tt(),M,N) -> mark#(N) -> mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) a__U12#(tt(),M,N) -> mark#(N) -> mark#(U11(X1,X2,X3)) -> mark#(X1) a__U12#(tt(),M,N) -> mark#(M) -> mark#(s(X)) -> mark#(X) a__U12#(tt(),M,N) -> mark#(M) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) a__U12#(tt(),M,N) -> mark#(M) -> mark#(x(X1,X2)) -> mark#(X1) a__U12#(tt(),M,N) -> mark#(M) -> mark#(x(X1,X2)) -> mark#(X2) a__U12#(tt(),M,N) -> mark#(M) -> mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) a__U12#(tt(),M,N) -> mark#(M) -> mark#(U22(X1,X2,X3)) -> mark#(X1) a__U12#(tt(),M,N) -> mark#(M) -> mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) a__U12#(tt(),M,N) -> mark#(M) -> mark#(U21(X1,X2,X3)) -> mark#(X1) a__U12#(tt(),M,N) -> mark#(M) -> mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) a__U12#(tt(),M,N) -> mark#(M) -> mark#(plus(X1,X2)) -> mark#(X1) a__U12#(tt(),M,N) -> mark#(M) -> mark#(plus(X1,X2)) -> mark#(X2) a__U12#(tt(),M,N) -> mark#(M) -> mark#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) a__U12#(tt(),M,N) -> mark#(M) -> mark#(U12(X1,X2,X3)) -> mark#(X1) a__U12#(tt(),M,N) -> mark#(M) -> mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) a__U12#(tt(),M,N) -> mark#(M) -> mark#(U11(X1,X2,X3)) -> mark#(X1) a__U11#(tt(),M,N) -> a__U12#(tt(),M,N) -> a__U12#(tt(),M,N) -> a__plus#(mark(N),mark(M)) a__U11#(tt(),M,N) -> a__U12#(tt(),M,N) -> a__U12#(tt(),M,N) -> mark#(N) a__U11#(tt(),M,N) -> a__U12#(tt(),M,N) -> a__U12#(tt(),M,N) -> mark#(M) Arctic Interpretation Processor: dimension: 1 interpretation: [a__x#](x0, x1) = x0 + x1 + 0, [a__U22#](x0, x1, x2) = x0 + x1 + x2 + 0, [a__U21#](x0, x1, x2) = x0 + x1 + x2 + 0, [a__plus#](x0, x1) = x0 + x1 + 0, [mark#](x0) = x0 + 0, [a__U12#](x0, x1, x2) = x0 + x1 + x2 + 0, [a__U11#](x0, x1, x2) = 1x0 + x1 + x2 + 0, [x](x0, x1) = x0 + x1, [U22](x0, x1, x2) = x0 + x1 + x2 + 0, [U21](x0, x1, x2) = x0 + x1 + x2, [plus](x0, x1) = x0 + x1, [U12](x0, x1, x2) = x0 + x1 + x2 + 1, [U11](x0, x1, x2) = 1x0 + x1 + x2 + 1, [0] = 0, [a__x](x0, x1) = x0 + x1 + 0, [a__U22](x0, x1, x2) = x0 + x1 + x2 + 0, [a__U21](x0, x1, x2) = x0 + x1 + x2 + 0, [s](x0) = x0 + 1, [a__plus](x0, x1) = x0 + x1 + 0, [mark](x0) = x0 + 0, [a__U12](x0, x1, x2) = x0 + x1 + x2 + 1, [a__U11](x0, x1, x2) = 1x0 + x1 + x2 + 1, [tt] = 0 orientation: a__U11#(tt(),M,N) = M + N + 1 >= M + N + 0 = a__U12#(tt(),M,N) a__U12#(tt(),M,N) = M + N + 0 >= M + 0 = mark#(M) a__U12#(tt(),M,N) = M + N + 0 >= N + 0 = mark#(N) a__U12#(tt(),M,N) = M + N + 0 >= M + N + 0 = a__plus#(mark(N),mark(M)) a__U21#(tt(),M,N) = M + N + 0 >= M + N + 0 = a__U22#(tt(),M,N) a__U22#(tt(),M,N) = M + N + 0 >= M + 0 = mark#(M) a__U22#(tt(),M,N) = M + N + 0 >= N + 0 = mark#(N) a__U22#(tt(),M,N) = M + N + 0 >= M + N + 0 = a__x#(mark(N),mark(M)) a__U22#(tt(),M,N) = M + N + 0 >= M + N + 0 = a__plus#(a__x(mark(N),mark(M)),mark(N)) a__plus#(N,0()) = N + 0 >= N + 0 = mark#(N) a__plus#(N,s(M)) = M + N + 1 >= M + N + 1 = a__U11#(tt(),M,N) a__x#(N,s(M)) = M + N + 1 >= M + N + 0 = a__U21#(tt(),M,N) mark#(U11(X1,X2,X3)) = 1X1 + X2 + X3 + 1 >= X1 + 0 = mark#(X1) mark#(U11(X1,X2,X3)) = 1X1 + X2 + X3 + 1 >= 1X1 + X2 + X3 + 1 = a__U11#(mark(X1),X2,X3) mark#(U12(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + 0 = mark#(X1) mark#(U12(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 0 = a__U12#(mark(X1),X2,X3) mark#(plus(X1,X2)) = X1 + X2 + 0 >= X2 + 0 = mark#(X2) mark#(plus(X1,X2)) = X1 + X2 + 0 >= X1 + 0 = mark#(X1) mark#(plus(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = a__plus#(mark(X1),mark(X2)) mark#(U21(X1,X2,X3)) = X1 + X2 + X3 + 0 >= X1 + 0 = mark#(X1) mark#(U21(X1,X2,X3)) = X1 + X2 + X3 + 0 >= X1 + X2 + X3 + 0 = a__U21#(mark(X1),X2,X3) mark#(U22(X1,X2,X3)) = X1 + X2 + X3 + 0 >= X1 + 0 = mark#(X1) mark#(U22(X1,X2,X3)) = X1 + X2 + X3 + 0 >= X1 + X2 + X3 + 0 = a__U22#(mark(X1),X2,X3) mark#(x(X1,X2)) = X1 + X2 + 0 >= X2 + 0 = mark#(X2) mark#(x(X1,X2)) = X1 + X2 + 0 >= X1 + 0 = mark#(X1) mark#(x(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = a__x#(mark(X1),mark(X2)) mark#(s(X)) = X + 1 >= X + 0 = mark#(X) a__U11(tt(),M,N) = M + N + 1 >= M + N + 1 = a__U12(tt(),M,N) a__U12(tt(),M,N) = M + N + 1 >= M + N + 1 = s(a__plus(mark(N),mark(M))) a__U21(tt(),M,N) = M + N + 0 >= M + N + 0 = a__U22(tt(),M,N) a__U22(tt(),M,N) = M + N + 0 >= M + N + 0 = a__plus(a__x(mark(N),mark(M)),mark(N)) a__plus(N,0()) = N + 0 >= N + 0 = mark(N) a__plus(N,s(M)) = M + N + 1 >= M + N + 1 = a__U11(tt(),M,N) a__x(N,0()) = N + 0 >= 0 = 0() a__x(N,s(M)) = M + N + 1 >= M + N + 0 = a__U21(tt(),M,N) mark(U11(X1,X2,X3)) = 1X1 + X2 + X3 + 1 >= 1X1 + X2 + X3 + 1 = a__U11(mark(X1),X2,X3) mark(U12(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = a__U12(mark(X1),X2,X3) mark(plus(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = a__plus(mark(X1),mark(X2)) mark(U21(X1,X2,X3)) = X1 + X2 + X3 + 0 >= X1 + X2 + X3 + 0 = a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) = X1 + X2 + X3 + 0 >= X1 + X2 + X3 + 0 = a__U22(mark(X1),X2,X3) mark(x(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = a__x(mark(X1),mark(X2)) mark(tt()) = 0 >= 0 = tt() mark(s(X)) = X + 1 >= X + 1 = s(mark(X)) mark(0()) = 0 >= 0 = 0() a__U11(X1,X2,X3) = 1X1 + X2 + X3 + 1 >= 1X1 + X2 + X3 + 1 = U11(X1,X2,X3) a__U12(X1,X2,X3) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = U12(X1,X2,X3) a__plus(X1,X2) = X1 + X2 + 0 >= X1 + X2 = plus(X1,X2) a__U21(X1,X2,X3) = X1 + X2 + X3 + 0 >= X1 + X2 + X3 = U21(X1,X2,X3) a__U22(X1,X2,X3) = X1 + X2 + X3 + 0 >= X1 + X2 + X3 + 0 = U22(X1,X2,X3) a__x(X1,X2) = X1 + X2 + 0 >= X1 + X2 = x(X1,X2) problem: DPs: a__U11#(tt(),M,N) -> a__U12#(tt(),M,N) a__U12#(tt(),M,N) -> mark#(M) a__U12#(tt(),M,N) -> mark#(N) a__U12#(tt(),M,N) -> a__plus#(mark(N),mark(M)) a__U21#(tt(),M,N) -> a__U22#(tt(),M,N) a__U22#(tt(),M,N) -> mark#(M) a__U22#(tt(),M,N) -> mark#(N) a__U22#(tt(),M,N) -> a__x#(mark(N),mark(M)) a__U22#(tt(),M,N) -> a__plus#(a__x(mark(N),mark(M)),mark(N)) a__plus#(N,0()) -> mark#(N) a__plus#(N,s(M)) -> a__U11#(tt(),M,N) a__x#(N,s(M)) -> a__U21#(tt(),M,N) mark#(U11(X1,X2,X3)) -> a__U11#(mark(X1),X2,X3) mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(U12(X1,X2,X3)) -> a__U12#(mark(X1),X2,X3) mark#(plus(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) mark#(U21(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2,X3)) -> a__U21#(mark(X1),X2,X3) mark#(U22(X1,X2,X3)) -> mark#(X1) mark#(U22(X1,X2,X3)) -> a__U22#(mark(X1),X2,X3) mark#(x(X1,X2)) -> mark#(X2) mark#(x(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) mark#(s(X)) -> mark#(X) TRS: a__U11(tt(),M,N) -> a__U12(tt(),M,N) a__U12(tt(),M,N) -> s(a__plus(mark(N),mark(M))) a__U21(tt(),M,N) -> a__U22(tt(),M,N) a__U22(tt(),M,N) -> a__plus(a__x(mark(N),mark(M)),mark(N)) a__plus(N,0()) -> mark(N) a__plus(N,s(M)) -> a__U11(tt(),M,N) a__x(N,0()) -> 0() a__x(N,s(M)) -> a__U21(tt(),M,N) mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3) mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3) mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2)) mark(U21(X1,X2,X3)) -> a__U21(mark(X1),X2,X3) mark(U22(X1,X2,X3)) -> a__U22(mark(X1),X2,X3) mark(x(X1,X2)) -> a__x(mark(X1),mark(X2)) mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(0()) -> 0() a__U11(X1,X2,X3) -> U11(X1,X2,X3) a__U12(X1,X2,X3) -> U12(X1,X2,X3) a__plus(X1,X2) -> plus(X1,X2) a__U21(X1,X2,X3) -> U21(X1,X2,X3) a__U22(X1,X2,X3) -> U22(X1,X2,X3) a__x(X1,X2) -> x(X1,X2) Open