YES Problem: op(i(x),op(y,z)) -> op(x,op(i(i(y)),z)) op(i(x),op(y,op(z,w))) -> op(x,op(z,op(y,w))) i(x) -> x Proof: DP Processor: DPs: op#(i(x),op(y,z)) -> i#(y) op#(i(x),op(y,z)) -> i#(i(y)) op#(i(x),op(y,z)) -> op#(i(i(y)),z) op#(i(x),op(y,z)) -> op#(x,op(i(i(y)),z)) op#(i(x),op(y,op(z,w))) -> op#(y,w) op#(i(x),op(y,op(z,w))) -> op#(z,op(y,w)) op#(i(x),op(y,op(z,w))) -> op#(x,op(z,op(y,w))) TRS: op(i(x),op(y,z)) -> op(x,op(i(i(y)),z)) op(i(x),op(y,op(z,w))) -> op(x,op(z,op(y,w))) i(x) -> x KBO Processor: argument filtering: pi(i) = [0] pi(op) = [0,1] pi(op#) = [0,1] pi(i#) = [0] usable rules: op(i(x),op(y,z)) -> op(x,op(i(i(y)),z)) op(i(x),op(y,op(z,w))) -> op(x,op(z,op(y,w))) i(x) -> x weight function: w0 = 1 w(i#) = w(op#) = 1 w(op) = w(i) = 0 precedence: i# ~ op# ~ op ~ i problem: DPs: TRS: op(i(x),op(y,z)) -> op(x,op(i(i(y)),z)) op(i(x),op(y,op(z,w))) -> op(x,op(z,op(y,w))) i(x) -> x Qed