YES Problem: c(c(c(a(x,y)))) -> b(c(c(c(c(y)))),x) c(c(b(c(y),0()))) -> a(0(),c(c(a(y,0())))) c(c(a(a(y,0()),x))) -> c(y) Proof: DP Processor: DPs: c#(c(c(a(x,y)))) -> c#(y) c#(c(c(a(x,y)))) -> c#(c(y)) c#(c(c(a(x,y)))) -> c#(c(c(y))) c#(c(c(a(x,y)))) -> c#(c(c(c(y)))) c#(c(b(c(y),0()))) -> c#(a(y,0())) c#(c(b(c(y),0()))) -> c#(c(a(y,0()))) c#(c(a(a(y,0()),x))) -> c#(y) TRS: c(c(c(a(x,y)))) -> b(c(c(c(c(y)))),x) c(c(b(c(y),0()))) -> a(0(),c(c(a(y,0())))) c(c(a(a(y,0()),x))) -> c(y) Matrix Interpretation Processor: dim=1 interpretation: [c#](x0) = 2x0 + 3, [0] = 0, [b](x0, x1) = x0 + 4, [c](x0) = 2x0, [a](x0, x1) = x0 + 2x1 + 1 orientation: c#(c(c(a(x,y)))) = 8x + 16y + 11 >= 2y + 3 = c#(y) c#(c(c(a(x,y)))) = 8x + 16y + 11 >= 4y + 3 = c#(c(y)) c#(c(c(a(x,y)))) = 8x + 16y + 11 >= 8y + 3 = c#(c(c(y))) c#(c(c(a(x,y)))) = 8x + 16y + 11 >= 16y + 3 = c#(c(c(c(y)))) c#(c(b(c(y),0()))) = 8y + 19 >= 2y + 5 = c#(a(y,0())) c#(c(b(c(y),0()))) = 8y + 19 >= 4y + 7 = c#(c(a(y,0()))) c#(c(a(a(y,0()),x))) = 8x + 4y + 11 >= 2y + 3 = c#(y) c(c(c(a(x,y)))) = 8x + 16y + 8 >= 16y + 4 = b(c(c(c(c(y)))),x) c(c(b(c(y),0()))) = 8y + 16 >= 8y + 9 = a(0(),c(c(a(y,0())))) c(c(a(a(y,0()),x))) = 8x + 4y + 8 >= 2y = c(y) problem: DPs: TRS: c(c(c(a(x,y)))) -> b(c(c(c(c(y)))),x) c(c(b(c(y),0()))) -> a(0(),c(c(a(y,0())))) c(c(a(a(y,0()),x))) -> c(y) Qed