YES Problem: f(f(a(),a()),x) -> f(a(),f(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#(x,f(a(),f(a(),a()))) f#(f(a(),a()),x) -> f#(a(),f(x,f(a(),f(a(),a())))) TRS: f(f(a(),a()),x) -> f(a(),f(x,f(a(),f(a(),a())))) EDG Processor: DPs: f#(f(a(),a()),x) -> f#(a(),f(a(),a())) f#(f(a(),a()),x) -> f#(x,f(a(),f(a(),a()))) f#(f(a(),a()),x) -> f#(a(),f(x,f(a(),f(a(),a())))) TRS: f(f(a(),a()),x) -> f(a(),f(x,f(a(),f(a(),a())))) graph: f#(f(a(),a()),x) -> f#(x,f(a(),f(a(),a()))) -> f#(f(a(),a()),x) -> f#(a(),f(a(),a())) f#(f(a(),a()),x) -> f#(x,f(a(),f(a(),a()))) -> f#(f(a(),a()),x) -> f#(x,f(a(),f(a(),a()))) f#(f(a(),a()),x) -> f#(x,f(a(),f(a(),a()))) -> f#(f(a(),a()),x) -> f#(a(),f(x,f(a(),f(a(),a())))) SCC Processor: #sccs: 1 #rules: 1 #arcs: 3/9 DPs: f#(f(a(),a()),x) -> f#(x,f(a(),f(a(),a()))) TRS: f(f(a(),a()),x) -> f(a(),f(x,f(a(),f(a(),a())))) Bounds Processor: bound: 0 enrichment: match automaton: final states: {6,1} transitions: f30() -> 5* f{#,0}(4,4) -> 1* f{#,0}(5,4) -> 1* f0(4,4) -> 8* f0(2,3) -> 4* f0(2,7) -> 6* f0(5,4) -> 7* f0(2,2) -> 3* f0(2,8) -> 7* a0() -> 2* problem: DPs: TRS: f(f(a(),a()),x) -> f(a(),f(x,f(a(),f(a(),a())))) Qed