MAYBE Problem: f(f(a(),a()),x) -> f(f(a(),x),f(a(),f(a(),a()))) Proof: DP Processor: DPs: f#(f(a(),a()),x) -> f#(a(),f(a(),a())) f#(f(a(),a()),x) -> f#(a(),x) f#(f(a(),a()),x) -> f#(f(a(),x),f(a(),f(a(),a()))) TRS: f(f(a(),a()),x) -> f(f(a(),x),f(a(),f(a(),a()))) Usable Rule Processor: DPs: f#(f(a(),a()),x) -> f#(a(),f(a(),a())) f#(f(a(),a()),x) -> f#(a(),x) f#(f(a(),a()),x) -> f#(f(a(),x),f(a(),f(a(),a()))) TRS: Restore Modifier: DPs: f#(f(a(),a()),x) -> f#(a(),f(a(),a())) f#(f(a(),a()),x) -> f#(a(),x) f#(f(a(),a()),x) -> f#(f(a(),x),f(a(),f(a(),a()))) TRS: f(f(a(),a()),x) -> f(f(a(),x),f(a(),f(a(),a()))) SCC Processor: #sccs: 1 #rules: 3 #arcs: 9/9 DPs: f#(f(a(),a()),x) -> f#(a(),f(a(),a())) f#(f(a(),a()),x) -> f#(a(),x) f#(f(a(),a()),x) -> f#(f(a(),x),f(a(),f(a(),a()))) TRS: f(f(a(),a()),x) -> f(f(a(),x),f(a(),f(a(),a()))) Matrix Interpretation Processor: dimension: 1 interpretation: [f#](x0, x1) = x0, [f](x0, x1) = x0 + 1, [a] = 1 orientation: f#(f(a(),a()),x) = 2 >= 1 = f#(a(),f(a(),a())) f#(f(a(),a()),x) = 2 >= 1 = f#(a(),x) f#(f(a(),a()),x) = 2 >= 2 = f#(f(a(),x),f(a(),f(a(),a()))) f(f(a(),a()),x) = 3 >= 3 = f(f(a(),x),f(a(),f(a(),a()))) problem: DPs: f#(f(a(),a()),x) -> f#(f(a(),x),f(a(),f(a(),a()))) TRS: f(f(a(),a()),x) -> f(f(a(),x),f(a(),f(a(),a()))) Open