MAYBE Problem: f(tt(),x) -> f(isDouble(x),s(s(x))) isDouble(s(s(x))) -> isDouble(x) isDouble(0()) -> tt() Proof: DP Processor: DPs: f#(tt(),x) -> isDouble#(x) f#(tt(),x) -> f#(isDouble(x),s(s(x))) isDouble#(s(s(x))) -> isDouble#(x) TRS: f(tt(),x) -> f(isDouble(x),s(s(x))) isDouble(s(s(x))) -> isDouble(x) isDouble(0()) -> tt() TDG Processor: DPs: f#(tt(),x) -> isDouble#(x) f#(tt(),x) -> f#(isDouble(x),s(s(x))) isDouble#(s(s(x))) -> isDouble#(x) TRS: f(tt(),x) -> f(isDouble(x),s(s(x))) isDouble(s(s(x))) -> isDouble(x) isDouble(0()) -> tt() graph: isDouble#(s(s(x))) -> isDouble#(x) -> isDouble#(s(s(x))) -> isDouble#(x) f#(tt(),x) -> isDouble#(x) -> isDouble#(s(s(x))) -> isDouble#(x) f#(tt(),x) -> f#(isDouble(x),s(s(x))) -> f#(tt(),x) -> f#(isDouble(x),s(s(x))) f#(tt(),x) -> f#(isDouble(x),s(s(x))) -> f#(tt(),x) -> isDouble#(x) SCC Processor: #sccs: 2 #rules: 2 #arcs: 4/9 DPs: f#(tt(),x) -> f#(isDouble(x),s(s(x))) TRS: f(tt(),x) -> f(isDouble(x),s(s(x))) isDouble(s(s(x))) -> isDouble(x) isDouble(0()) -> tt() Open DPs: isDouble#(s(s(x))) -> isDouble#(x) TRS: f(tt(),x) -> f(isDouble(x),s(s(x))) isDouble(s(s(x))) -> isDouble(x) isDouble(0()) -> tt() KBO Processor: argument filtering: pi(tt) = [] pi(f) = [] pi(isDouble) = 0 pi(s) = [0] pi(0) = [] pi(isDouble#) = [0] weight function: w0 = 1 w(isDouble#) = w(0) = w(f) = w(tt) = 1 w(s) = w(isDouble) = 0 precedence: s ~ f > 0 > isDouble# ~ isDouble ~ tt problem: DPs: TRS: f(tt(),x) -> f(isDouble(x),s(s(x))) isDouble(s(s(x))) -> isDouble(x) isDouble(0()) -> tt() Qed