YES Problem: f(x,y,w,w,a()) -> g1(x,x,y,w) f(x,y,w,a(),a()) -> g1(y,x,x,w) f(x,y,a(),a(),w) -> g2(x,y,y,w) f(x,y,a(),w,w) -> g2(y,y,x,w) g1(x,x,y,a()) -> h(x,y) g1(y,x,x,a()) -> h(x,y) g2(x,y,y,a()) -> h(x,y) g2(y,y,x,a()) -> h(x,y) h(x,x) -> x Proof: Bounds Processor: bound: 2 enrichment: roof automaton: final states: {6,1,2} transitions: f0(6,1,2,2,2) -> 1* f0(1,1,2,2,2) -> 1* f0(2,1,2,2,2) -> 1* f0(6,2,2,2,2) -> 1* f0(1,2,2,2,2) -> 1* f0(2,2,2,2,2) -> 1* f0(1,6,2,2,2) -> 1* f0(6,6,2,2,2) -> 1* f0(2,6,2,2,2) -> 1* f0(1,1,2,6,2) -> 1* f0(6,1,2,6,2) -> 1* f0(2,1,2,6,2) -> 1* f0(1,2,2,6,2) -> 1* f0(6,2,2,6,2) -> 1* f0(2,2,2,6,2) -> 1* f0(1,1,6,2,1) -> 1* f0(6,1,6,2,1) -> 1* f0(2,1,6,2,1) -> 1* f0(1,2,6,2,1) -> 1* f0(6,2,6,2,1) -> 1* f0(2,2,6,2,1) -> 1* f0(1,6,2,6,2) -> 1* f0(6,6,2,6,2) -> 1* f0(2,6,2,6,2) -> 1* f0(6,1,1,2,1) -> 1* f0(1,6,6,2,1) -> 1* f0(6,6,6,2,1) -> 1* f0(2,6,6,2,1) -> 1* f0(1,1,1,2,1) -> 1* f0(2,1,1,2,1) -> 1* f0(6,2,1,2,1) -> 1* f0(1,2,1,2,1) -> 1* f0(2,2,1,2,1) -> 1* f0(1,6,1,2,1) -> 1* f0(6,6,1,2,1) -> 1* f0(2,6,1,2,1) -> 1* f0(1,1,6,6,1) -> 1* f0(6,1,6,6,1) -> 1* f0(2,1,6,6,1) -> 1* f0(1,2,6,6,1) -> 1* f0(6,2,6,6,1) -> 1* f0(2,2,6,6,1) -> 1* f0(1,1,1,6,1) -> 1* f0(6,1,1,6,1) -> 1* f0(2,1,1,6,1) -> 1* f0(1,6,6,6,1) -> 1* f0(6,6,6,6,1) -> 1* f0(2,6,6,6,1) -> 1* f0(1,2,1,6,1) -> 1* f0(6,2,1,6,1) -> 1* f0(2,2,1,6,1) -> 1* f0(1,6,1,6,1) -> 1* f0(6,6,1,6,1) -> 1* f0(2,6,1,6,1) -> 1* f0(6,1,2,1,1) -> 1* f0(1,1,2,1,1) -> 1* f0(2,1,2,1,1) -> 1* f0(6,2,2,1,1) -> 1* f0(1,2,2,1,1) -> 1* f0(2,2,2,1,1) -> 1* f0(1,6,2,1,1) -> 1* f0(6,6,2,1,1) -> 1* f0(2,6,2,1,1) -> 1* f0(1,1,6,1,6) -> 1* f0(6,1,6,1,6) -> 1* f0(2,1,6,1,6) -> 1* f0(1,2,6,1,6) -> 1* f0(6,2,6,1,6) -> 1* f0(2,2,6,1,6) -> 1* f0(1,1,1,1,6) -> 1* f0(6,1,1,1,6) -> 1* f0(2,1,1,1,6) -> 1* f0(1,6,6,1,6) -> 1* f0(6,6,6,1,6) -> 1* f0(2,6,6,1,6) -> 1* f0(1,2,1,1,6) -> 1* f0(6,2,1,1,6) -> 1* f0(2,2,1,1,6) -> 1* f0(1,6,1,1,6) -> 1* f0(6,6,1,1,6) -> 1* f0(2,6,1,1,6) -> 1* f0(1,1,2,2,6) -> 1* f0(6,1,2,2,6) -> 1* f0(2,1,2,2,6) -> 1* f0(1,2,2,2,6) -> 1* f0(6,2,2,2,6) -> 1* f0(2,2,2,2,6) -> 1* f0(1,6,2,2,6) -> 1* f0(6,6,2,2,6) -> 1* f0(2,6,2,2,6) -> 1* f0(1,1,2,6,6) -> 1* f0(6,1,2,6,6) -> 1* f0(2,1,2,6,6) -> 1* f0(1,2,2,6,6) -> 1* f0(6,2,2,6,6) -> 1* f0(2,2,2,6,6) -> 1* f0(1,6,2,6,6) -> 1* f0(6,6,2,6,6) -> 1* f0(2,6,2,6,6) -> 1* f0(1,1,6,2,2) -> 1* f0(6,1,6,2,2) -> 1* f0(2,1,6,2,2) -> 1* f0(1,2,6,2,2) -> 1* f0(6,2,6,2,2) -> 1* f0(2,2,6,2,2) -> 1* f0(6,1,1,2,2) -> 1* f0(1,6,6,2,2) -> 1* f0(6,6,6,2,2) -> 1* f0(2,6,6,2,2) -> 1* f0(1,1,1,2,2) -> 1* f0(2,1,1,2,2) -> 1* f0(6,2,1,2,2) -> 1* f0(1,2,1,2,2) -> 1* f0(2,2,1,2,2) -> 1* f0(1,6,1,2,2) -> 1* f0(6,6,1,2,2) -> 1* f0(2,6,1,2,2) -> 1* f0(1,1,6,6,2) -> 1* f0(6,1,6,6,2) -> 1* f0(2,1,6,6,2) -> 1* f0(1,2,6,6,2) -> 1* f0(6,2,6,6,2) -> 1* f0(2,2,6,6,2) -> 1* f0(1,1,1,6,2) -> 1* f0(6,1,1,6,2) -> 1* f0(2,1,1,6,2) -> 1* f0(1,6,6,6,2) -> 1* f0(6,6,6,6,2) -> 1* f0(2,6,6,6,2) -> 1* f0(1,2,1,6,2) -> 1* f0(6,2,1,6,2) -> 1* f0(2,2,1,6,2) -> 1* f0(1,6,1,6,2) -> 1* f0(6,6,1,6,2) -> 1* f0(2,6,1,6,2) -> 1* f0(6,1,2,1,2) -> 1* f0(1,1,2,1,2) -> 1* f0(2,1,2,1,2) -> 1* f0(6,2,2,1,2) -> 1* f0(1,2,2,1,2) -> 1* f0(2,2,2,1,2) -> 1* f0(1,6,2,1,2) -> 1* f0(6,6,2,1,2) -> 1* f0(2,6,2,1,2) -> 1* f0(1,1,6,1,1) -> 1* f0(6,1,6,1,1) -> 1* f0(2,1,6,1,1) -> 1* f0(1,2,6,1,1) -> 1* f0(6,2,6,1,1) -> 1* f0(2,2,6,1,1) -> 1* f0(6,1,1,1,1) -> 1* f0(1,6,6,1,1) -> 1* f0(6,6,6,1,1) -> 1* f0(2,6,6,1,1) -> 1* f0(1,1,1,1,1) -> 1* f0(2,1,1,1,1) -> 1* f0(6,2,1,1,1) -> 1* f0(1,2,1,1,1) -> 1* f0(2,2,1,1,1) -> 1* f0(1,6,1,1,1) -> 1* f0(6,6,1,1,1) -> 1* f0(2,6,1,1,1) -> 1* f0(6,1,2,2,1) -> 1* f0(1,1,2,2,1) -> 1* f0(2,1,2,2,1) -> 1* f0(6,2,2,2,1) -> 1* f0(1,2,2,2,1) -> 1* f0(2,2,2,2,1) -> 1* f0(1,6,2,2,1) -> 1* f0(6,6,2,2,1) -> 1* f0(2,6,2,2,1) -> 1* f0(1,1,2,6,1) -> 1* f0(6,1,2,6,1) -> 1* f0(2,1,2,6,1) -> 1* f0(1,2,2,6,1) -> 1* f0(6,2,2,6,1) -> 1* f0(2,2,2,6,1) -> 1* f0(1,6,2,6,1) -> 1* f0(6,6,2,6,1) -> 1* f0(2,6,2,6,1) -> 1* f0(1,1,6,2,6) -> 1* f0(6,1,6,2,6) -> 1* f0(2,1,6,2,6) -> 1* f0(1,2,6,2,6) -> 1* f0(6,2,6,2,6) -> 1* f0(2,2,6,2,6) -> 1* f0(1,1,1,2,6) -> 1* f0(6,1,1,2,6) -> 1* f0(2,1,1,2,6) -> 1* f0(1,6,6,2,6) -> 1* f0(6,6,6,2,6) -> 1* f0(2,6,6,2,6) -> 1* f0(1,2,1,2,6) -> 1* f0(6,2,1,2,6) -> 1* f0(2,2,1,2,6) -> 1* f0(1,6,1,2,6) -> 1* f0(6,6,1,2,6) -> 1* f0(2,6,1,2,6) -> 1* f0(1,1,6,6,6) -> 1* f0(6,1,6,6,6) -> 1* f0(2,1,6,6,6) -> 1* f0(1,2,6,6,6) -> 1* f0(6,2,6,6,6) -> 1* f0(2,2,6,6,6) -> 1* f0(1,1,1,6,6) -> 1* f0(6,1,1,6,6) -> 1* f0(2,1,1,6,6) -> 1* f0(1,6,6,6,6) -> 1* f0(6,6,6,6,6) -> 1* f0(2,6,6,6,6) -> 1* f0(1,2,1,6,6) -> 1* f0(6,2,1,6,6) -> 1* f0(2,2,1,6,6) -> 1* f0(1,6,1,6,6) -> 1* f0(6,6,1,6,6) -> 1* f0(2,6,1,6,6) -> 1* f0(1,1,2,1,6) -> 1* f0(6,1,2,1,6) -> 1* f0(2,1,2,1,6) -> 1* f0(1,2,2,1,6) -> 1* f0(6,2,2,1,6) -> 1* f0(2,2,2,1,6) -> 1* f0(1,6,2,1,6) -> 1* f0(6,6,2,1,6) -> 1* f0(2,6,2,1,6) -> 1* f0(1,1,6,1,2) -> 1* f0(6,1,6,1,2) -> 1* f0(2,1,6,1,2) -> 1* f0(1,2,6,1,2) -> 1* f0(6,2,6,1,2) -> 1* f0(2,2,6,1,2) -> 1* f0(6,1,1,1,2) -> 1* f0(1,6,6,1,2) -> 1* f0(6,6,6,1,2) -> 1* f0(2,6,6,1,2) -> 1* f0(1,1,1,1,2) -> 1* f0(2,1,1,1,2) -> 1* f0(6,2,1,1,2) -> 1* f0(1,2,1,1,2) -> 1* f0(2,2,1,1,2) -> 1* f0(1,6,1,1,2) -> 1* f0(6,6,1,1,2) -> 1* f0(2,6,1,1,2) -> 1* a0() -> 6*,1,2 g10(6,6,6,6) -> 1* g10(1,6,6,6) -> 1* g10(2,2,1,2) -> 1* g10(2,1,6,2) -> 1* g10(2,6,1,2) -> 1* g10(2,1,1,1) -> 1* g10(2,1,6,6) -> 1* g10(2,2,6,1) -> 1* g10(2,6,6,1) -> 1* g10(6,1,2,2) -> 1* g10(1,1,2,2) -> 1* g10(6,1,2,6) -> 1* g10(6,2,2,1) -> 1* g10(1,1,2,6) -> 1* g10(1,2,2,1) -> 1* g10(6,6,2,1) -> 1* g10(1,6,2,1) -> 1* g10(2,2,2,2) -> 1* g10(2,6,2,2) -> 1* g10(2,1,2,1) -> 1* g10(2,2,2,6) -> 1* g10(2,6,2,6) -> 1* g10(6,2,1,6) -> 1* g10(1,2,1,6) -> 1* g10(6,6,1,6) -> 1* g10(1,6,1,6) -> 1* g10(2,1,1,6) -> 1* g10(6,2,1,2) -> 1* g10(1,2,1,2) -> 1* g10(6,1,6,2) -> 1* g10(6,6,1,2) -> 1* g10(1,1,6,2) -> 1* g10(1,6,1,2) -> 1* g10(6,1,1,1) -> 1* g10(1,1,1,1) -> 1* g10(6,1,6,6) -> 1* g10(6,2,6,1) -> 1* g10(1,1,6,6) -> 1* g10(1,2,6,1) -> 1* g10(6,6,6,1) -> 1* g10(1,6,6,1) -> 1* g10(2,1,1,2) -> 1* g10(2,2,6,2) -> 1* g10(2,2,1,1) -> 1* g10(2,6,6,2) -> 1* g10(2,1,6,1) -> 1* g10(2,6,1,1) -> 1* g10(2,2,6,6) -> 1* g10(2,6,6,6) -> 1* g10(6,2,2,2) -> 1* g10(1,2,2,2) -> 1* g10(6,6,2,2) -> 1* g10(1,6,2,2) -> 1* g10(6,1,2,1) -> 1* g10(1,1,2,1) -> 1* g10(6,2,2,6) -> 1* g10(1,2,2,6) -> 1* g10(6,6,2,6) -> 1* g10(1,6,2,6) -> 1* g10(2,1,2,2) -> 1* g10(2,1,2,6) -> 1* g10(2,2,2,1) -> 1* g10(6,1,1,6) -> 1* g10(2,6,2,1) -> 1* g10(1,1,1,6) -> 1* g10(2,2,1,6) -> 1* g10(2,6,1,6) -> 1* g10(6,1,1,2) -> 1* g10(1,1,1,2) -> 1* g10(6,2,6,2) -> 1* g10(1,2,6,2) -> 1* g10(6,2,1,1) -> 1* g10(1,2,1,1) -> 1* g10(6,6,6,2) -> 1* g10(1,6,6,2) -> 1* g10(6,1,6,1) -> 1* g10(6,6,1,1) -> 1* g10(1,1,6,1) -> 1* g10(6,2,6,6) -> 1* g10(1,6,1,1) -> 1* g10(1,2,6,6) -> 1* g20(6,6,6,6) -> 1* g20(1,6,6,6) -> 1* g20(2,2,1,2) -> 1* g20(2,1,6,2) -> 1* g20(2,6,1,2) -> 1* g20(2,1,1,1) -> 1* g20(2,1,6,6) -> 1* g20(2,2,6,1) -> 1* g20(2,6,6,1) -> 1* g20(6,1,2,2) -> 1* g20(1,1,2,2) -> 1* g20(6,1,2,6) -> 1* g20(6,2,2,1) -> 1* g20(1,1,2,6) -> 1* g20(1,2,2,1) -> 1* g20(6,6,2,1) -> 1* g20(1,6,2,1) -> 1* g20(2,2,2,2) -> 1* g20(2,6,2,2) -> 1* g20(2,1,2,1) -> 1* g20(2,2,2,6) -> 1* g20(2,6,2,6) -> 1* g20(6,2,1,6) -> 1* g20(1,2,1,6) -> 1* g20(6,6,1,6) -> 1* g20(1,6,1,6) -> 1* g20(2,1,1,6) -> 1* g20(6,2,1,2) -> 1* g20(1,2,1,2) -> 1* g20(6,1,6,2) -> 1* g20(6,6,1,2) -> 1* g20(1,1,6,2) -> 1* g20(1,6,1,2) -> 1* g20(6,1,1,1) -> 1* g20(1,1,1,1) -> 1* g20(6,1,6,6) -> 1* g20(6,2,6,1) -> 1* g20(1,1,6,6) -> 1* g20(1,2,6,1) -> 1* g20(6,6,6,1) -> 1* g20(1,6,6,1) -> 1* g20(2,1,1,2) -> 1* g20(2,2,6,2) -> 1* g20(2,2,1,1) -> 1* g20(2,6,6,2) -> 1* g20(2,1,6,1) -> 1* g20(2,6,1,1) -> 1* g20(2,2,6,6) -> 1* g20(2,6,6,6) -> 1* g20(6,2,2,2) -> 1* g20(1,2,2,2) -> 1* g20(6,6,2,2) -> 1* g20(1,6,2,2) -> 1* g20(6,1,2,1) -> 1* g20(1,1,2,1) -> 1* g20(6,2,2,6) -> 1* g20(1,2,2,6) -> 1* g20(6,6,2,6) -> 1* g20(1,6,2,6) -> 1* g20(2,1,2,2) -> 1* g20(2,1,2,6) -> 1* g20(2,2,2,1) -> 1* g20(6,1,1,6) -> 1* g20(2,6,2,1) -> 1* g20(1,1,1,6) -> 1* g20(2,2,1,6) -> 1* g20(2,6,1,6) -> 1* g20(6,1,1,2) -> 1* g20(1,1,1,2) -> 1* g20(6,2,6,2) -> 1* g20(1,2,6,2) -> 1* g20(6,2,1,1) -> 1* g20(1,2,1,1) -> 1* g20(6,6,6,2) -> 1* g20(1,6,6,2) -> 1* g20(6,1,6,1) -> 1* g20(6,6,1,1) -> 1* g20(1,1,6,1) -> 1* g20(6,2,6,6) -> 1* g20(1,6,1,1) -> 1* g20(1,2,6,6) -> 1* h0(6,2) -> 1* h0(1,2) -> 1* h0(6,6) -> 1* h0(1,6) -> 1* h0(2,1) -> 1* h0(6,1) -> 1* h0(1,1) -> 1* h0(2,2) -> 1* h0(2,6) -> 1* h1(6,2) -> 1* h1(1,2) -> 1* h1(6,6) -> 1* h1(1,6) -> 1* h1(2,1) -> 1* h1(6,1) -> 1* h1(1,1) -> 1* h1(2,2) -> 1* h1(2,6) -> 1* g21(6,6,6,6) -> 1* g21(1,6,6,6) -> 1* g21(2,2,1,2) -> 1* g21(2,1,6,2) -> 1* g21(2,6,1,2) -> 1* g21(2,1,1,1) -> 1* g21(2,1,6,6) -> 1* g21(2,2,6,1) -> 1* g21(2,6,6,1) -> 1* g21(6,1,2,2) -> 1* g21(1,1,2,2) -> 1* g21(6,1,2,6) -> 1* g21(6,2,2,1) -> 1* g21(1,1,2,6) -> 1* g21(1,2,2,1) -> 1* g21(6,6,2,1) -> 1* g21(1,6,2,1) -> 1* g21(2,2,2,2) -> 1* g21(2,6,2,2) -> 1* g21(2,2,2,6) -> 1* g21(2,6,2,6) -> 1* g21(6,2,1,6) -> 1* g21(6,6,1,6) -> 1* g21(1,6,1,6) -> 1* g21(2,1,1,6) -> 1* g21(6,2,1,2) -> 1* g21(6,1,6,2) -> 1* g21(6,6,1,2) -> 1* g21(1,1,6,2) -> 1* g21(1,6,1,2) -> 1* g21(6,1,1,1) -> 1* g21(1,1,1,1) -> 1* g21(6,1,6,6) -> 1* g21(6,2,6,1) -> 1* g21(1,1,6,6) -> 1* g21(1,2,6,1) -> 1* g21(6,6,6,1) -> 1* g21(1,6,6,1) -> 1* g21(2,1,1,2) -> 1* g21(2,2,6,2) -> 1* g21(2,2,1,1) -> 1* g21(2,6,6,2) -> 1* g21(2,1,6,1) -> 1* g21(2,6,1,1) -> 1* g21(2,2,6,6) -> 1* g21(2,6,6,6) -> 1* g21(6,2,2,2) -> 1* g21(1,2,2,2) -> 1* g21(6,6,2,2) -> 1* g21(1,6,2,2) -> 1* g21(6,1,2,1) -> 1* g21(1,1,2,1) -> 1* g21(6,2,2,6) -> 1* g21(1,2,2,6) -> 1* g21(6,6,2,6) -> 1* g21(1,6,2,6) -> 1* g21(2,2,2,1) -> 1* g21(6,1,1,6) -> 1* g21(2,6,2,1) -> 1* g21(1,1,1,6) -> 1* g21(2,2,1,6) -> 1* g21(2,6,1,6) -> 1* g21(6,1,1,2) -> 1* g21(1,1,1,2) -> 1* g21(6,2,6,2) -> 1* g21(1,2,6,2) -> 1* g21(6,2,1,1) -> 1* g21(6,6,6,2) -> 1* g21(1,6,6,2) -> 1* g21(6,1,6,1) -> 1* g21(6,6,1,1) -> 1* g21(1,1,6,1) -> 1* g21(6,2,6,6) -> 1* g21(1,6,1,1) -> 1* g21(1,2,6,6) -> 1* g11(6,6,6,6) -> 1* g11(1,6,6,6) -> 1* g11(2,2,1,2) -> 1* g11(2,1,6,2) -> 1* g11(2,6,1,2) -> 1* g11(2,1,1,1) -> 1* g11(2,1,6,6) -> 1* g11(2,2,6,1) -> 1* g11(2,6,6,1) -> 1* g11(6,1,2,2) -> 1* g11(1,1,2,2) -> 1* g11(6,1,2,6) -> 1* g11(6,2,2,1) -> 1* g11(1,1,2,6) -> 1* g11(1,2,2,1) -> 1* g11(6,6,2,1) -> 1* g11(1,6,2,1) -> 1* g11(2,2,2,2) -> 1* g11(2,6,2,2) -> 1* g11(2,2,2,6) -> 1* g11(2,6,2,6) -> 1* g11(6,2,1,6) -> 1* g11(6,6,1,6) -> 1* g11(1,6,1,6) -> 1* g11(2,1,1,6) -> 1* g11(6,2,1,2) -> 1* g11(6,1,6,2) -> 1* g11(6,6,1,2) -> 1* g11(1,1,6,2) -> 1* g11(1,6,1,2) -> 1* g11(6,1,1,1) -> 1* g11(1,1,1,1) -> 1* g11(6,1,6,6) -> 1* g11(6,2,6,1) -> 1* g11(1,1,6,6) -> 1* g11(1,2,6,1) -> 1* g11(6,6,6,1) -> 1* g11(1,6,6,1) -> 1* g11(2,1,1,2) -> 1* g11(2,2,6,2) -> 1* g11(2,2,1,1) -> 1* g11(2,6,6,2) -> 1* g11(2,1,6,1) -> 1* g11(2,6,1,1) -> 1* g11(2,2,6,6) -> 1* g11(2,6,6,6) -> 1* g11(6,2,2,2) -> 1* g11(1,2,2,2) -> 1* g11(6,6,2,2) -> 1* g11(1,6,2,2) -> 1* g11(6,1,2,1) -> 1* g11(1,1,2,1) -> 1* g11(6,2,2,6) -> 1* g11(1,2,2,6) -> 1* g11(6,6,2,6) -> 1* g11(1,6,2,6) -> 1* g11(2,2,2,1) -> 1* g11(6,1,1,6) -> 1* g11(2,6,2,1) -> 1* g11(1,1,1,6) -> 1* g11(2,2,1,6) -> 1* g11(2,6,1,6) -> 1* g11(6,1,1,2) -> 1* g11(1,1,1,2) -> 1* g11(6,2,6,2) -> 1* g11(1,2,6,2) -> 1* g11(6,2,1,1) -> 1* g11(6,6,6,2) -> 1* g11(1,6,6,2) -> 1* g11(6,1,6,1) -> 1* g11(6,6,1,1) -> 1* g11(1,1,6,1) -> 1* g11(6,2,6,6) -> 1* g11(1,6,1,1) -> 1* g11(1,2,6,6) -> 1* h2(6,2) -> 1* h2(6,6) -> 1* h2(1,6) -> 1* h2(2,1) -> 1* h2(6,1) -> 1* h2(1,1) -> 1* h2(2,6) -> 1* 2 -> 1* 6 -> 1* problem: Qed