YES Problem: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(plus(N,0())) -> mark(N) active(plus(N,s(M))) -> mark(U11(tt(),M,N)) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(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,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(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: Matrix Interpretation Processor: dim=1 interpretation: [0] = 0, [s](x0) = x0 + 6, [plus](x0, x1) = x0 + 2x1, [mark](x0) = x0, [U12](x0, x1, x2) = 2x0 + 2x1 + x2 + 4, [active](x0) = x0, [U11](x0, x1, x2) = 2x0 + 2x1 + x2 + 4, [tt] = 1 orientation: active(U11(tt(),M,N)) = 2M + N + 6 >= 2M + N + 6 = mark(U12(tt(),M,N)) active(U12(tt(),M,N)) = 2M + N + 6 >= 2M + N + 6 = mark(s(plus(N,M))) active(plus(N,0())) = N >= N = mark(N) active(plus(N,s(M))) = 2M + N + 12 >= 2M + N + 6 = mark(U11(tt(),M,N)) mark(U11(X1,X2,X3)) = 2X1 + 2X2 + X3 + 4 >= 2X1 + 2X2 + X3 + 4 = active(U11(mark(X1),X2,X3)) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X1,X2,X3)) = 2X1 + 2X2 + X3 + 4 >= 2X1 + 2X2 + X3 + 4 = active(U12(mark(X1),X2,X3)) mark(s(X)) = X + 6 >= X + 6 = active(s(mark(X))) mark(plus(X1,X2)) = X1 + 2X2 >= X1 + 2X2 = active(plus(mark(X1),mark(X2))) mark(0()) = 0 >= 0 = active(0()) U11(mark(X1),X2,X3) = 2X1 + 2X2 + X3 + 4 >= 2X1 + 2X2 + X3 + 4 = U11(X1,X2,X3) U11(X1,mark(X2),X3) = 2X1 + 2X2 + X3 + 4 >= 2X1 + 2X2 + X3 + 4 = U11(X1,X2,X3) U11(X1,X2,mark(X3)) = 2X1 + 2X2 + X3 + 4 >= 2X1 + 2X2 + X3 + 4 = U11(X1,X2,X3) U11(active(X1),X2,X3) = 2X1 + 2X2 + X3 + 4 >= 2X1 + 2X2 + X3 + 4 = U11(X1,X2,X3) U11(X1,active(X2),X3) = 2X1 + 2X2 + X3 + 4 >= 2X1 + 2X2 + X3 + 4 = U11(X1,X2,X3) U11(X1,X2,active(X3)) = 2X1 + 2X2 + X3 + 4 >= 2X1 + 2X2 + X3 + 4 = U11(X1,X2,X3) U12(mark(X1),X2,X3) = 2X1 + 2X2 + X3 + 4 >= 2X1 + 2X2 + X3 + 4 = U12(X1,X2,X3) U12(X1,mark(X2),X3) = 2X1 + 2X2 + X3 + 4 >= 2X1 + 2X2 + X3 + 4 = U12(X1,X2,X3) U12(X1,X2,mark(X3)) = 2X1 + 2X2 + X3 + 4 >= 2X1 + 2X2 + X3 + 4 = U12(X1,X2,X3) U12(active(X1),X2,X3) = 2X1 + 2X2 + X3 + 4 >= 2X1 + 2X2 + X3 + 4 = U12(X1,X2,X3) U12(X1,active(X2),X3) = 2X1 + 2X2 + X3 + 4 >= 2X1 + 2X2 + X3 + 4 = U12(X1,X2,X3) U12(X1,X2,active(X3)) = 2X1 + 2X2 + X3 + 4 >= 2X1 + 2X2 + X3 + 4 = U12(X1,X2,X3) s(mark(X)) = X + 6 >= X + 6 = s(X) s(active(X)) = X + 6 >= X + 6 = s(X) plus(mark(X1),X2) = X1 + 2X2 >= X1 + 2X2 = plus(X1,X2) plus(X1,mark(X2)) = X1 + 2X2 >= X1 + 2X2 = plus(X1,X2) plus(active(X1),X2) = X1 + 2X2 >= X1 + 2X2 = plus(X1,X2) plus(X1,active(X2)) = X1 + 2X2 >= X1 + 2X2 = plus(X1,X2) problem: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(plus(N,0())) -> mark(N) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(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,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(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) DP Processor: DPs: active#(U11(tt(),M,N)) -> U12#(tt(),M,N) active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) active#(U12(tt(),M,N)) -> plus#(N,M) active#(U12(tt(),M,N)) -> s#(plus(N,M)) active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) active#(plus(N,0())) -> mark#(N) mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2,X3)) -> U11#(mark(X1),X2,X3) mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) mark#(tt()) -> active#(tt()) mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(U12(X1,X2,X3)) -> U12#(mark(X1),X2,X3) mark#(U12(X1,X2,X3)) -> active#(U12(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,X3) -> U11#(X1,X2,X3) U11#(X1,mark(X2),X3) -> U11#(X1,X2,X3) U11#(X1,X2,mark(X3)) -> U11#(X1,X2,X3) U11#(active(X1),X2,X3) -> U11#(X1,X2,X3) U11#(X1,active(X2),X3) -> U11#(X1,X2,X3) U11#(X1,X2,active(X3)) -> U11#(X1,X2,X3) U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) U12#(X1,mark(X2),X3) -> U12#(X1,X2,X3) U12#(X1,X2,mark(X3)) -> U12#(X1,X2,X3) U12#(active(X1),X2,X3) -> U12#(X1,X2,X3) U12#(X1,active(X2),X3) -> U12#(X1,X2,X3) U12#(X1,X2,active(X3)) -> U12#(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(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(plus(N,0())) -> mark(N) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(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,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(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(),M,N)) -> U12#(tt(),M,N) active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) active#(U12(tt(),M,N)) -> plus#(N,M) active#(U12(tt(),M,N)) -> s#(plus(N,M)) active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) active#(plus(N,0())) -> mark#(N) mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2,X3)) -> U11#(mark(X1),X2,X3) mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) mark#(tt()) -> active#(tt()) mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(U12(X1,X2,X3)) -> U12#(mark(X1),X2,X3) mark#(U12(X1,X2,X3)) -> active#(U12(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,X3) -> U11#(X1,X2,X3) U11#(X1,mark(X2),X3) -> U11#(X1,X2,X3) U11#(X1,X2,mark(X3)) -> U11#(X1,X2,X3) U11#(active(X1),X2,X3) -> U11#(X1,X2,X3) U11#(X1,active(X2),X3) -> U11#(X1,X2,X3) U11#(X1,X2,active(X3)) -> U11#(X1,X2,X3) U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) U12#(X1,mark(X2),X3) -> U12#(X1,X2,X3) U12#(X1,X2,mark(X3)) -> U12#(X1,X2,X3) U12#(active(X1),X2,X3) -> U12#(X1,X2,X3) U12#(X1,active(X2),X3) -> U12#(X1,X2,X3) U12#(X1,X2,active(X3)) -> U12#(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(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(plus(N,0())) -> mark(N) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(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,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(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: U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) -> U11#(X1,X2,active(X3)) -> U11#(X1,X2,X3) U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) -> U11#(X1,active(X2),X3) -> U11#(X1,X2,X3) U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) -> U11#(active(X1),X2,X3) -> U11#(X1,X2,X3) U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) -> U11#(X1,X2,mark(X3)) -> U11#(X1,X2,X3) U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) -> U11#(X1,mark(X2),X3) -> U11#(X1,X2,X3) U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) -> U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) U11#(active(X1),X2,X3) -> U11#(X1,X2,X3) -> U11#(X1,X2,active(X3)) -> U11#(X1,X2,X3) U11#(active(X1),X2,X3) -> U11#(X1,X2,X3) -> U11#(X1,active(X2),X3) -> U11#(X1,X2,X3) U11#(active(X1),X2,X3) -> U11#(X1,X2,X3) -> U11#(active(X1),X2,X3) -> U11#(X1,X2,X3) U11#(active(X1),X2,X3) -> U11#(X1,X2,X3) -> U11#(X1,X2,mark(X3)) -> U11#(X1,X2,X3) U11#(active(X1),X2,X3) -> U11#(X1,X2,X3) -> U11#(X1,mark(X2),X3) -> U11#(X1,X2,X3) U11#(active(X1),X2,X3) -> U11#(X1,X2,X3) -> U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) U11#(X1,mark(X2),X3) -> U11#(X1,X2,X3) -> U11#(X1,X2,active(X3)) -> U11#(X1,X2,X3) U11#(X1,mark(X2),X3) -> U11#(X1,X2,X3) -> U11#(X1,active(X2),X3) -> U11#(X1,X2,X3) U11#(X1,mark(X2),X3) -> U11#(X1,X2,X3) -> U11#(active(X1),X2,X3) -> U11#(X1,X2,X3) U11#(X1,mark(X2),X3) -> U11#(X1,X2,X3) -> U11#(X1,X2,mark(X3)) -> U11#(X1,X2,X3) U11#(X1,mark(X2),X3) -> U11#(X1,X2,X3) -> U11#(X1,mark(X2),X3) -> U11#(X1,X2,X3) U11#(X1,mark(X2),X3) -> U11#(X1,X2,X3) -> U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) U11#(X1,active(X2),X3) -> U11#(X1,X2,X3) -> U11#(X1,X2,active(X3)) -> U11#(X1,X2,X3) U11#(X1,active(X2),X3) -> U11#(X1,X2,X3) -> U11#(X1,active(X2),X3) -> U11#(X1,X2,X3) U11#(X1,active(X2),X3) -> U11#(X1,X2,X3) -> U11#(active(X1),X2,X3) -> U11#(X1,X2,X3) U11#(X1,active(X2),X3) -> U11#(X1,X2,X3) -> U11#(X1,X2,mark(X3)) -> U11#(X1,X2,X3) U11#(X1,active(X2),X3) -> U11#(X1,X2,X3) -> U11#(X1,mark(X2),X3) -> U11#(X1,X2,X3) U11#(X1,active(X2),X3) -> U11#(X1,X2,X3) -> U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) U11#(X1,X2,mark(X3)) -> U11#(X1,X2,X3) -> U11#(X1,X2,active(X3)) -> U11#(X1,X2,X3) U11#(X1,X2,mark(X3)) -> U11#(X1,X2,X3) -> U11#(X1,active(X2),X3) -> U11#(X1,X2,X3) U11#(X1,X2,mark(X3)) -> U11#(X1,X2,X3) -> U11#(active(X1),X2,X3) -> U11#(X1,X2,X3) U11#(X1,X2,mark(X3)) -> U11#(X1,X2,X3) -> U11#(X1,X2,mark(X3)) -> U11#(X1,X2,X3) U11#(X1,X2,mark(X3)) -> U11#(X1,X2,X3) -> U11#(X1,mark(X2),X3) -> U11#(X1,X2,X3) U11#(X1,X2,mark(X3)) -> U11#(X1,X2,X3) -> U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) U11#(X1,X2,active(X3)) -> U11#(X1,X2,X3) -> U11#(X1,X2,active(X3)) -> U11#(X1,X2,X3) U11#(X1,X2,active(X3)) -> U11#(X1,X2,X3) -> U11#(X1,active(X2),X3) -> U11#(X1,X2,X3) U11#(X1,X2,active(X3)) -> U11#(X1,X2,X3) -> U11#(active(X1),X2,X3) -> U11#(X1,X2,X3) U11#(X1,X2,active(X3)) -> U11#(X1,X2,X3) -> U11#(X1,X2,mark(X3)) -> U11#(X1,X2,X3) U11#(X1,X2,active(X3)) -> U11#(X1,X2,X3) -> U11#(X1,mark(X2),X3) -> U11#(X1,X2,X3) U11#(X1,X2,active(X3)) -> U11#(X1,X2,X3) -> U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) 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#(0()) -> active#(0()) -> active#(plus(N,0())) -> mark#(N) mark#(0()) -> active#(0()) -> active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) mark#(0()) -> active#(0()) -> active#(U12(tt(),M,N)) -> s#(plus(N,M)) mark#(0()) -> active#(0()) -> active#(U12(tt(),M,N)) -> plus#(N,M) mark#(0()) -> active#(0()) -> active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) mark#(0()) -> active#(0()) -> active#(U11(tt(),M,N)) -> U12#(tt(),M,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#(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#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) mark#(s(X)) -> mark#(X) -> mark#(U12(X1,X2,X3)) -> U12#(mark(X1),X2,X3) mark#(s(X)) -> mark#(X) -> mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(tt()) -> active#(tt()) mark#(s(X)) -> mark#(X) -> mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) mark#(s(X)) -> mark#(X) -> mark#(U11(X1,X2,X3)) -> U11#(mark(X1),X2,X3) mark#(s(X)) -> mark#(X) -> mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(s(X)) -> active#(s(mark(X))) -> active#(plus(N,0())) -> mark#(N) mark#(s(X)) -> active#(s(mark(X))) -> active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) mark#(s(X)) -> active#(s(mark(X))) -> active#(U12(tt(),M,N)) -> s#(plus(N,M)) mark#(s(X)) -> active#(s(mark(X))) -> active#(U12(tt(),M,N)) -> plus#(N,M) mark#(s(X)) -> active#(s(mark(X))) -> active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) mark#(s(X)) -> active#(s(mark(X))) -> active#(U11(tt(),M,N)) -> U12#(tt(),M,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#(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#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U12(X1,X2,X3)) -> 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#(tt()) -> active#(tt()) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U11(X1,X2,X3)) -> 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#(0()) -> active#(0()) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(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#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U12(X1,X2,X3)) -> 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#(tt()) -> active#(tt()) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> U11#(mark(X1),X2,X3) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(plus(N,0())) -> mark#(N) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(U12(tt(),M,N)) -> s#(plus(N,M)) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(U12(tt(),M,N)) -> plus#(N,M) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(U11(tt(),M,N)) -> U12#(tt(),M,N) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> 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#(s(X)) -> active#(s(mark(X))) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(s(X)) -> s#(mark(X)) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X1,X2,X3)) -> 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#(tt()) -> active#(tt()) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> U11#(mark(X1),X2,X3) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(U12(X1,X2,X3)) -> U12#(mark(X1),X2,X3) -> U12#(X1,X2,active(X3)) -> U12#(X1,X2,X3) mark#(U12(X1,X2,X3)) -> U12#(mark(X1),X2,X3) -> U12#(X1,active(X2),X3) -> U12#(X1,X2,X3) mark#(U12(X1,X2,X3)) -> U12#(mark(X1),X2,X3) -> U12#(active(X1),X2,X3) -> U12#(X1,X2,X3) mark#(U12(X1,X2,X3)) -> U12#(mark(X1),X2,X3) -> U12#(X1,X2,mark(X3)) -> U12#(X1,X2,X3) mark#(U12(X1,X2,X3)) -> U12#(mark(X1),X2,X3) -> U12#(X1,mark(X2),X3) -> U12#(X1,X2,X3) mark#(U12(X1,X2,X3)) -> U12#(mark(X1),X2,X3) -> U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) -> active#(plus(N,0())) -> mark#(N) mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) -> active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) -> active#(U12(tt(),M,N)) -> s#(plus(N,M)) mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) -> active#(U12(tt(),M,N)) -> plus#(N,M) mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) -> active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) -> active#(U11(tt(),M,N)) -> U12#(tt(),M,N) mark#(U11(X1,X2,X3)) -> U11#(mark(X1),X2,X3) -> U11#(X1,X2,active(X3)) -> U11#(X1,X2,X3) mark#(U11(X1,X2,X3)) -> U11#(mark(X1),X2,X3) -> U11#(X1,active(X2),X3) -> U11#(X1,X2,X3) mark#(U11(X1,X2,X3)) -> U11#(mark(X1),X2,X3) -> U11#(active(X1),X2,X3) -> U11#(X1,X2,X3) mark#(U11(X1,X2,X3)) -> U11#(mark(X1),X2,X3) -> U11#(X1,X2,mark(X3)) -> U11#(X1,X2,X3) mark#(U11(X1,X2,X3)) -> U11#(mark(X1),X2,X3) -> U11#(X1,mark(X2),X3) -> U11#(X1,X2,X3) mark#(U11(X1,X2,X3)) -> U11#(mark(X1),X2,X3) -> U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> 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#(s(X)) -> active#(s(mark(X))) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(s(X)) -> s#(mark(X)) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X1,X2,X3)) -> 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#(tt()) -> active#(tt()) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> U11#(mark(X1),X2,X3) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) -> active#(plus(N,0())) -> mark#(N) mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) -> active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) -> active#(U12(tt(),M,N)) -> s#(plus(N,M)) mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) -> active#(U12(tt(),M,N)) -> plus#(N,M) mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) -> active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) -> active#(U11(tt(),M,N)) -> U12#(tt(),M,N) mark#(tt()) -> active#(tt()) -> active#(plus(N,0())) -> mark#(N) mark#(tt()) -> active#(tt()) -> active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) mark#(tt()) -> active#(tt()) -> active#(U12(tt(),M,N)) -> s#(plus(N,M)) mark#(tt()) -> active#(tt()) -> active#(U12(tt(),M,N)) -> plus#(N,M) mark#(tt()) -> active#(tt()) -> active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) mark#(tt()) -> active#(tt()) -> active#(U11(tt(),M,N)) -> U12#(tt(),M,N) U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) -> U12#(X1,X2,active(X3)) -> U12#(X1,X2,X3) U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) -> U12#(X1,active(X2),X3) -> U12#(X1,X2,X3) U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) -> U12#(active(X1),X2,X3) -> U12#(X1,X2,X3) U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) -> U12#(X1,X2,mark(X3)) -> U12#(X1,X2,X3) U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) -> U12#(X1,mark(X2),X3) -> U12#(X1,X2,X3) U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) -> U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) U12#(active(X1),X2,X3) -> U12#(X1,X2,X3) -> U12#(X1,X2,active(X3)) -> U12#(X1,X2,X3) U12#(active(X1),X2,X3) -> U12#(X1,X2,X3) -> U12#(X1,active(X2),X3) -> U12#(X1,X2,X3) U12#(active(X1),X2,X3) -> U12#(X1,X2,X3) -> U12#(active(X1),X2,X3) -> U12#(X1,X2,X3) U12#(active(X1),X2,X3) -> U12#(X1,X2,X3) -> U12#(X1,X2,mark(X3)) -> U12#(X1,X2,X3) U12#(active(X1),X2,X3) -> U12#(X1,X2,X3) -> U12#(X1,mark(X2),X3) -> U12#(X1,X2,X3) U12#(active(X1),X2,X3) -> U12#(X1,X2,X3) -> U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) U12#(X1,mark(X2),X3) -> U12#(X1,X2,X3) -> U12#(X1,X2,active(X3)) -> U12#(X1,X2,X3) U12#(X1,mark(X2),X3) -> U12#(X1,X2,X3) -> U12#(X1,active(X2),X3) -> U12#(X1,X2,X3) U12#(X1,mark(X2),X3) -> U12#(X1,X2,X3) -> U12#(active(X1),X2,X3) -> U12#(X1,X2,X3) U12#(X1,mark(X2),X3) -> U12#(X1,X2,X3) -> U12#(X1,X2,mark(X3)) -> U12#(X1,X2,X3) U12#(X1,mark(X2),X3) -> U12#(X1,X2,X3) -> U12#(X1,mark(X2),X3) -> U12#(X1,X2,X3) U12#(X1,mark(X2),X3) -> U12#(X1,X2,X3) -> U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) U12#(X1,active(X2),X3) -> U12#(X1,X2,X3) -> U12#(X1,X2,active(X3)) -> U12#(X1,X2,X3) U12#(X1,active(X2),X3) -> U12#(X1,X2,X3) -> U12#(X1,active(X2),X3) -> U12#(X1,X2,X3) U12#(X1,active(X2),X3) -> U12#(X1,X2,X3) -> U12#(active(X1),X2,X3) -> U12#(X1,X2,X3) U12#(X1,active(X2),X3) -> U12#(X1,X2,X3) -> U12#(X1,X2,mark(X3)) -> U12#(X1,X2,X3) U12#(X1,active(X2),X3) -> U12#(X1,X2,X3) -> U12#(X1,mark(X2),X3) -> U12#(X1,X2,X3) U12#(X1,active(X2),X3) -> U12#(X1,X2,X3) -> U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) U12#(X1,X2,mark(X3)) -> U12#(X1,X2,X3) -> U12#(X1,X2,active(X3)) -> U12#(X1,X2,X3) U12#(X1,X2,mark(X3)) -> U12#(X1,X2,X3) -> U12#(X1,active(X2),X3) -> U12#(X1,X2,X3) U12#(X1,X2,mark(X3)) -> U12#(X1,X2,X3) -> U12#(active(X1),X2,X3) -> U12#(X1,X2,X3) U12#(X1,X2,mark(X3)) -> U12#(X1,X2,X3) -> U12#(X1,X2,mark(X3)) -> U12#(X1,X2,X3) U12#(X1,X2,mark(X3)) -> U12#(X1,X2,X3) -> U12#(X1,mark(X2),X3) -> U12#(X1,X2,X3) U12#(X1,X2,mark(X3)) -> U12#(X1,X2,X3) -> U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) U12#(X1,X2,active(X3)) -> U12#(X1,X2,X3) -> U12#(X1,X2,active(X3)) -> U12#(X1,X2,X3) U12#(X1,X2,active(X3)) -> U12#(X1,X2,X3) -> U12#(X1,active(X2),X3) -> U12#(X1,X2,X3) U12#(X1,X2,active(X3)) -> U12#(X1,X2,X3) -> U12#(active(X1),X2,X3) -> U12#(X1,X2,X3) U12#(X1,X2,active(X3)) -> U12#(X1,X2,X3) -> U12#(X1,X2,mark(X3)) -> U12#(X1,X2,X3) U12#(X1,X2,active(X3)) -> U12#(X1,X2,X3) -> U12#(X1,mark(X2),X3) -> U12#(X1,X2,X3) U12#(X1,X2,active(X3)) -> U12#(X1,X2,X3) -> U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) active#(plus(N,0())) -> mark#(N) -> mark#(0()) -> active#(0()) active#(plus(N,0())) -> mark#(N) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(plus(N,0())) -> mark#(N) -> mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) active#(plus(N,0())) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X1) active#(plus(N,0())) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X2) active#(plus(N,0())) -> mark#(N) -> mark#(s(X)) -> active#(s(mark(X))) active#(plus(N,0())) -> mark#(N) -> mark#(s(X)) -> s#(mark(X)) active#(plus(N,0())) -> mark#(N) -> mark#(s(X)) -> mark#(X) active#(plus(N,0())) -> mark#(N) -> mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) active#(plus(N,0())) -> mark#(N) -> mark#(U12(X1,X2,X3)) -> U12#(mark(X1),X2,X3) active#(plus(N,0())) -> mark#(N) -> mark#(U12(X1,X2,X3)) -> mark#(X1) active#(plus(N,0())) -> mark#(N) -> mark#(tt()) -> active#(tt()) active#(plus(N,0())) -> mark#(N) -> mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) active#(plus(N,0())) -> mark#(N) -> mark#(U11(X1,X2,X3)) -> U11#(mark(X1),X2,X3) active#(plus(N,0())) -> mark#(N) -> mark#(U11(X1,X2,X3)) -> mark#(X1) active#(U12(tt(),M,N)) -> s#(plus(N,M)) -> s#(active(X)) -> s#(X) active#(U12(tt(),M,N)) -> s#(plus(N,M)) -> s#(mark(X)) -> s#(X) active#(U12(tt(),M,N)) -> plus#(N,M) -> plus#(X1,active(X2)) -> plus#(X1,X2) active#(U12(tt(),M,N)) -> plus#(N,M) -> plus#(active(X1),X2) -> plus#(X1,X2) active#(U12(tt(),M,N)) -> plus#(N,M) -> plus#(X1,mark(X2)) -> plus#(X1,X2) active#(U12(tt(),M,N)) -> plus#(N,M) -> plus#(mark(X1),X2) -> plus#(X1,X2) active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(0()) -> active#(0()) active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(plus(X1,X2)) -> mark#(X1) active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(plus(X1,X2)) -> mark#(X2) active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(s(X)) -> active#(s(mark(X))) active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(s(X)) -> s#(mark(X)) active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(s(X)) -> mark#(X) active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(U12(X1,X2,X3)) -> U12#(mark(X1),X2,X3) active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(U12(X1,X2,X3)) -> mark#(X1) active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(tt()) -> active#(tt()) active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(U11(X1,X2,X3)) -> U11#(mark(X1),X2,X3) active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(U11(X1,X2,X3)) -> mark#(X1) active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) -> mark#(0()) -> active#(0()) active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) -> mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) -> mark#(plus(X1,X2)) -> mark#(X1) active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) -> mark#(plus(X1,X2)) -> mark#(X2) active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) -> mark#(s(X)) -> active#(s(mark(X))) active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) -> mark#(s(X)) -> s#(mark(X)) active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) -> mark#(s(X)) -> mark#(X) active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) -> mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) -> mark#(U12(X1,X2,X3)) -> U12#(mark(X1),X2,X3) active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) -> mark#(U12(X1,X2,X3)) -> mark#(X1) active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) -> mark#(tt()) -> active#(tt()) active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) -> mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) -> mark#(U11(X1,X2,X3)) -> U11#(mark(X1),X2,X3) active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) -> mark#(U11(X1,X2,X3)) -> mark#(X1) active#(U11(tt(),M,N)) -> U12#(tt(),M,N) -> U12#(X1,X2,active(X3)) -> U12#(X1,X2,X3) active#(U11(tt(),M,N)) -> U12#(tt(),M,N) -> U12#(X1,active(X2),X3) -> U12#(X1,X2,X3) active#(U11(tt(),M,N)) -> U12#(tt(),M,N) -> U12#(active(X1),X2,X3) -> U12#(X1,X2,X3) active#(U11(tt(),M,N)) -> U12#(tt(),M,N) -> U12#(X1,X2,mark(X3)) -> U12#(X1,X2,X3) active#(U11(tt(),M,N)) -> U12#(tt(),M,N) -> U12#(X1,mark(X2),X3) -> U12#(X1,X2,X3) active#(U11(tt(),M,N)) -> U12#(tt(),M,N) -> U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) SCC Processor: #sccs: 5 #rules: 32 #arcs: 278/1521 DPs: mark#(0()) -> active#(0()) active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) mark#(tt()) -> active#(tt()) active#(plus(N,0())) -> mark#(N) mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) mark#(s(X)) -> 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)) -> active#(plus(mark(X1),mark(X2))) TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(plus(N,0())) -> mark(N) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(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,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(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) EDG Processor: DPs: mark#(0()) -> active#(0()) active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) mark#(tt()) -> active#(tt()) active#(plus(N,0())) -> mark#(N) mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) mark#(s(X)) -> 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)) -> active#(plus(mark(X1),mark(X2))) TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(plus(N,0())) -> mark(N) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(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,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(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: mark#(s(X)) -> mark#(X) -> mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) mark#(s(X)) -> mark#(X) -> mark#(tt()) -> active#(tt()) mark#(s(X)) -> mark#(X) -> mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> active#(s(mark(X))) mark#(s(X)) -> mark#(X) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(s(X)) -> mark#(X) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(s(X)) -> mark#(X) -> mark#(0()) -> active#(0()) mark#(s(X)) -> active#(s(mark(X))) -> active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) mark#(s(X)) -> active#(s(mark(X))) -> active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) mark#(s(X)) -> active#(s(mark(X))) -> active#(plus(N,0())) -> mark#(N) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(tt()) -> active#(tt()) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> active#(s(mark(X))) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(plus(X1,X2)) -> mark#(X2) -> mark#(0()) -> active#(0()) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(tt()) -> active#(tt()) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> active#(s(mark(X))) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(plus(X1,X2)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) -> active#(plus(N,0())) -> mark#(N) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(tt()) -> active#(tt()) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(s(X)) -> active#(s(mark(X))) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> 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)) -> active#(plus(mark(X1),mark(X2))) mark#(U12(X1,X2,X3)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) -> active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) -> active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) -> active#(plus(N,0())) -> mark#(N) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(tt()) -> active#(tt()) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(s(X)) -> active#(s(mark(X))) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(plus(X1,X2)) -> 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)) -> active#(plus(mark(X1),mark(X2))) mark#(U11(X1,X2,X3)) -> mark#(X1) -> mark#(0()) -> active#(0()) mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) -> active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) -> active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) -> active#(plus(N,0())) -> mark#(N) active#(plus(N,0())) -> mark#(N) -> mark#(U11(X1,X2,X3)) -> mark#(X1) active#(plus(N,0())) -> mark#(N) -> mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) active#(plus(N,0())) -> mark#(N) -> mark#(tt()) -> active#(tt()) active#(plus(N,0())) -> mark#(N) -> mark#(U12(X1,X2,X3)) -> mark#(X1) active#(plus(N,0())) -> mark#(N) -> mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) active#(plus(N,0())) -> mark#(N) -> mark#(s(X)) -> mark#(X) active#(plus(N,0())) -> mark#(N) -> mark#(s(X)) -> active#(s(mark(X))) active#(plus(N,0())) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X2) active#(plus(N,0())) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X1) active#(plus(N,0())) -> mark#(N) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(plus(N,0())) -> mark#(N) -> mark#(0()) -> active#(0()) active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(U11(X1,X2,X3)) -> mark#(X1) active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(U12(X1,X2,X3)) -> mark#(X1) active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(s(X)) -> mark#(X) active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(s(X)) -> active#(s(mark(X))) active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(plus(X1,X2)) -> mark#(X2) active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(plus(X1,X2)) -> mark#(X1) active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) -> mark#(U11(X1,X2,X3)) -> mark#(X1) active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) -> mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) -> mark#(U12(X1,X2,X3)) -> mark#(X1) active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) -> mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) -> mark#(s(X)) -> mark#(X) active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) -> mark#(s(X)) -> active#(s(mark(X))) active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) -> mark#(plus(X1,X2)) -> mark#(X2) active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) -> mark#(plus(X1,X2)) -> mark#(X1) active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) -> mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) SCC Processor: #sccs: 1 #rules: 12 #arcs: 96/196 DPs: mark#(s(X)) -> mark#(X) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(plus(N,0())) -> mark#(N) mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X2) mark#(s(X)) -> active#(s(mark(X))) active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) mark#(U11(X1,X2,X3)) -> mark#(X1) TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(plus(N,0())) -> mark(N) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(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,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(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) Arctic Interpretation Processor: dimension: 1 interpretation: [mark#](x0) = x0, [active#](x0) = x0 + 0, [0] = 0, [s](x0) = x0 + 0, [plus](x0, x1) = x0 + x1 + 7, [mark](x0) = x0, [U12](x0, x1, x2) = x0 + x1 + x2 + 7, [active](x0) = x0, [U11](x0, x1, x2) = 7x0 + x1 + x2 + 4, [tt] = 0 orientation: mark#(s(X)) = X + 0 >= X = mark#(X) mark#(plus(X1,X2)) = X1 + X2 + 7 >= X1 + X2 + 7 = active#(plus(mark(X1),mark(X2))) active#(plus(N,0())) = N + 7 >= N = mark#(N) mark#(plus(X1,X2)) = X1 + X2 + 7 >= X1 = mark#(X1) mark#(plus(X1,X2)) = X1 + X2 + 7 >= X2 = mark#(X2) mark#(s(X)) = X + 0 >= X + 0 = active#(s(mark(X))) active#(U12(tt(),M,N)) = M + N + 7 >= M + N + 7 = mark#(s(plus(N,M))) mark#(U12(X1,X2,X3)) = X1 + X2 + X3 + 7 >= X1 + X2 + X3 + 7 = active#(U12(mark(X1),X2,X3)) active#(U11(tt(),M,N)) = M + N + 7 >= M + N + 7 = mark#(U12(tt(),M,N)) mark#(U12(X1,X2,X3)) = X1 + X2 + X3 + 7 >= X1 = mark#(X1) mark#(U11(X1,X2,X3)) = 7X1 + X2 + X3 + 4 >= 7X1 + X2 + X3 + 4 = active#(U11(mark(X1),X2,X3)) mark#(U11(X1,X2,X3)) = 7X1 + X2 + X3 + 4 >= X1 = mark#(X1) active(U11(tt(),M,N)) = M + N + 7 >= M + N + 7 = mark(U12(tt(),M,N)) active(U12(tt(),M,N)) = M + N + 7 >= M + N + 7 = mark(s(plus(N,M))) active(plus(N,0())) = N + 7 >= N = mark(N) mark(U11(X1,X2,X3)) = 7X1 + X2 + X3 + 4 >= 7X1 + X2 + X3 + 4 = active(U11(mark(X1),X2,X3)) mark(tt()) = 0 >= 0 = active(tt()) mark(U12(X1,X2,X3)) = X1 + X2 + X3 + 7 >= X1 + X2 + X3 + 7 = active(U12(mark(X1),X2,X3)) mark(s(X)) = X + 0 >= X + 0 = active(s(mark(X))) mark(plus(X1,X2)) = X1 + X2 + 7 >= X1 + X2 + 7 = active(plus(mark(X1),mark(X2))) mark(0()) = 0 >= 0 = active(0()) U11(mark(X1),X2,X3) = 7X1 + X2 + X3 + 4 >= 7X1 + X2 + X3 + 4 = U11(X1,X2,X3) U11(X1,mark(X2),X3) = 7X1 + X2 + X3 + 4 >= 7X1 + X2 + X3 + 4 = U11(X1,X2,X3) U11(X1,X2,mark(X3)) = 7X1 + X2 + X3 + 4 >= 7X1 + X2 + X3 + 4 = U11(X1,X2,X3) U11(active(X1),X2,X3) = 7X1 + X2 + X3 + 4 >= 7X1 + X2 + X3 + 4 = U11(X1,X2,X3) U11(X1,active(X2),X3) = 7X1 + X2 + X3 + 4 >= 7X1 + X2 + X3 + 4 = U11(X1,X2,X3) U11(X1,X2,active(X3)) = 7X1 + X2 + X3 + 4 >= 7X1 + X2 + X3 + 4 = U11(X1,X2,X3) U12(mark(X1),X2,X3) = X1 + X2 + X3 + 7 >= X1 + X2 + X3 + 7 = U12(X1,X2,X3) U12(X1,mark(X2),X3) = X1 + X2 + X3 + 7 >= X1 + X2 + X3 + 7 = U12(X1,X2,X3) U12(X1,X2,mark(X3)) = X1 + X2 + X3 + 7 >= X1 + X2 + X3 + 7 = U12(X1,X2,X3) U12(active(X1),X2,X3) = X1 + X2 + X3 + 7 >= X1 + X2 + X3 + 7 = U12(X1,X2,X3) U12(X1,active(X2),X3) = X1 + X2 + X3 + 7 >= X1 + X2 + X3 + 7 = U12(X1,X2,X3) U12(X1,X2,active(X3)) = X1 + X2 + X3 + 7 >= X1 + X2 + X3 + 7 = U12(X1,X2,X3) s(mark(X)) = X + 0 >= X + 0 = s(X) s(active(X)) = X + 0 >= X + 0 = s(X) plus(mark(X1),X2) = X1 + X2 + 7 >= X1 + X2 + 7 = plus(X1,X2) plus(X1,mark(X2)) = X1 + X2 + 7 >= X1 + X2 + 7 = plus(X1,X2) plus(active(X1),X2) = X1 + X2 + 7 >= X1 + X2 + 7 = plus(X1,X2) plus(X1,active(X2)) = X1 + X2 + 7 >= X1 + X2 + 7 = plus(X1,X2) problem: DPs: mark#(s(X)) -> mark#(X) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(plus(N,0())) -> mark#(N) mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X2) mark#(s(X)) -> active#(s(mark(X))) active#(U12(tt(),M,N)) -> mark#(s(plus(N,M))) mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) active#(U11(tt(),M,N)) -> mark#(U12(tt(),M,N)) mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(plus(N,0())) -> mark(N) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(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,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(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) KBO Processor: argument filtering: pi(tt) = [] pi(U11) = [1,2] pi(active) = 0 pi(U12) = [0,1,2] pi(mark) = 0 pi(plus) = [0,1] pi(s) = 0 pi(0) = [] pi(active#) = 0 pi(mark#) = 0 weight function: w0 = 1 w(mark#) = w(0) = w(active) = w(U11) = w(tt) = 1 w(active#) = w(s) = w(plus) = w(mark) = w(U12) = 0 precedence: U11 > mark# ~ active# ~ 0 ~ s ~ plus ~ mark ~ U12 ~ active ~ tt problem: DPs: mark#(s(X)) -> mark#(X) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(s(X)) -> active#(s(mark(X))) mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(plus(N,0())) -> mark(N) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(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,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(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) SCC Processor: #sccs: 1 #rules: 1 #arcs: 84/25 DPs: mark#(s(X)) -> mark#(X) TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(plus(N,0())) -> mark(N) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(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,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(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) Subterm Criterion Processor: simple projection: pi(mark#) = 0 problem: DPs: TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(plus(N,0())) -> mark(N) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(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,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(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) Qed DPs: U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) U12#(X1,mark(X2),X3) -> U12#(X1,X2,X3) U12#(X1,X2,mark(X3)) -> U12#(X1,X2,X3) U12#(active(X1),X2,X3) -> U12#(X1,X2,X3) U12#(X1,active(X2),X3) -> U12#(X1,X2,X3) U12#(X1,X2,active(X3)) -> U12#(X1,X2,X3) TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(plus(N,0())) -> mark(N) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(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,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(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) Subterm Criterion Processor: simple projection: pi(U12#) = 2 problem: DPs: U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) U12#(X1,mark(X2),X3) -> U12#(X1,X2,X3) U12#(active(X1),X2,X3) -> U12#(X1,X2,X3) U12#(X1,active(X2),X3) -> U12#(X1,X2,X3) TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(plus(N,0())) -> mark(N) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(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,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(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) Subterm Criterion Processor: simple projection: pi(U12#) = 1 problem: DPs: U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) U12#(active(X1),X2,X3) -> U12#(X1,X2,X3) TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(plus(N,0())) -> mark(N) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(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,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(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) Subterm Criterion Processor: simple projection: pi(U12#) = 0 problem: DPs: TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(plus(N,0())) -> mark(N) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(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,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(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) Qed 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(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(plus(N,0())) -> mark(N) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(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,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(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) Subterm Criterion Processor: simple projection: pi(plus#) = 1 problem: DPs: plus#(mark(X1),X2) -> plus#(X1,X2) plus#(active(X1),X2) -> plus#(X1,X2) TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(plus(N,0())) -> mark(N) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(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,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(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) Subterm Criterion Processor: simple projection: pi(plus#) = 0 problem: DPs: TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(plus(N,0())) -> mark(N) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(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,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(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) Qed DPs: s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(plus(N,0())) -> mark(N) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(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,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(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) Subterm Criterion Processor: simple projection: pi(s#) = 0 problem: DPs: TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(plus(N,0())) -> mark(N) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(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,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(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) Qed DPs: U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) U11#(X1,mark(X2),X3) -> U11#(X1,X2,X3) U11#(X1,X2,mark(X3)) -> U11#(X1,X2,X3) U11#(active(X1),X2,X3) -> U11#(X1,X2,X3) U11#(X1,active(X2),X3) -> U11#(X1,X2,X3) U11#(X1,X2,active(X3)) -> U11#(X1,X2,X3) TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(plus(N,0())) -> mark(N) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(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,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(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) Subterm Criterion Processor: simple projection: pi(U11#) = 2 problem: DPs: U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) U11#(X1,mark(X2),X3) -> U11#(X1,X2,X3) U11#(active(X1),X2,X3) -> U11#(X1,X2,X3) U11#(X1,active(X2),X3) -> U11#(X1,X2,X3) TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(plus(N,0())) -> mark(N) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(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,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(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) Subterm Criterion Processor: simple projection: pi(U11#) = 1 problem: DPs: U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) U11#(active(X1),X2,X3) -> U11#(X1,X2,X3) TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(plus(N,0())) -> mark(N) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(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,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(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) Subterm Criterion Processor: simple projection: pi(U11#) = 0 problem: DPs: TRS: active(U11(tt(),M,N)) -> mark(U12(tt(),M,N)) active(U12(tt(),M,N)) -> mark(s(plus(N,M))) active(plus(N,0())) -> mark(N) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(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,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(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) Qed