/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: sum(cons(s(n),x),cons(m,y)) -> sum(cons(n,x),cons(s(m),y)) sum(cons(0(),x),y) -> sum(x,y) sum(nil(),y) -> y weight(cons(n,cons(m,x))) -> weight(sum(cons(n,cons(m,x)),cons(0(),x))) weight(cons(n,nil())) -> n Proof: Matrix Interpretation Processor: dim=3 interpretation: [0] [nil] = [1] [0], [1 1 1] [1 0 0] [cons](x0, x1) = [0 1 0]x0 + [1 1 0]x1 [0 0 0] [1 0 0] , [0] [0] = [0] [0], [1 1 0] [weight](x0) = [0 1 0]x0 [1 1 0] , [1 0 1] [1] [s](x0) = [0 0 0]x0 + [0] [0 1 0] [1], [1 0 0] [sum](x0, x1) = [0 0 0]x0 + x1 [1 0 0] orientation: [1 1 1] [1 1 1] [1 0 0] [1 0 0] [2] [1 1 1] [1 1 1] [1 0 0] [1 0 0] [2] sum(cons(s(n),x),cons(m,y)) = [0 1 0]m + [0 0 0]n + [0 0 0]x + [1 1 0]y + [0] >= [0 0 0]m + [0 0 0]n + [0 0 0]x + [1 1 0]y + [0] = sum(cons(n,x),cons(s(m),y)) [0 0 0] [1 1 1] [1 0 0] [1 0 0] [2] [0 0 0] [1 1 1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] sum(cons(0(),x),y) = [0 0 0]x + y >= [0 0 0]x + y = sum(x,y) [1 0 0] [1 0 0] sum(nil(),y) = y >= y = y [2 3 2] [1 2 1] [3 1 0] [1 1 1] [1 1 1] [3 1 0] weight(cons(n,cons(m,x))) = [1 2 1]m + [0 1 0]n + [2 1 0]x >= [0 0 0]m + [0 0 0]n + [1 1 0]x = weight(sum(cons(n,cons(m,x)),cons(0(),x))) [2 3 2] [1 2 1] [3 1 0] [1 1 1] [1 1 1] [3 1 0] [1 2 1] [1] weight(cons(n,nil())) = [0 1 0]n + [1] >= n = n [1 2 1] [1] problem: sum(cons(s(n),x),cons(m,y)) -> sum(cons(n,x),cons(s(m),y)) sum(cons(0(),x),y) -> sum(x,y) sum(nil(),y) -> y weight(cons(n,cons(m,x))) -> weight(sum(cons(n,cons(m,x)),cons(0(),x))) Matrix Interpretation Processor: dim=3 interpretation: [1] [nil] = [0] [0], [1 0 1] [1 0 0] [cons](x0, x1) = [0 0 0]x0 + [0 0 1]x1 [0 0 0] [1 1 1] , [0] [0] = [0] [0], [1 1 0] [weight](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1] [s](x0) = [0 0 0]x0 + [0] [0 0 1] [1], [1 0 0] [1 0 0] [sum](x0, x1) = [0 0 0]x0 + [0 1 0]x1 [1 0 0] [1 1 1] orientation: [1 0 1] [1 0 1] [1 0 0] [1 0 0] [2] [1 0 1] [1 0 1] [1 0 0] [1 0 0] [2] sum(cons(s(n),x),cons(m,y)) = [0 0 0]m + [0 0 0]n + [0 0 0]x + [0 0 1]y + [0] >= [0 0 0]m + [0 0 0]n + [0 0 0]x + [0 0 1]y + [0] = sum(cons(n,x),cons(s(m),y)) [1 0 1] [1 0 1] [1 0 0] [2 1 2] [2] [1 0 1] [1 0 1] [1 0 0] [2 1 2] [2] [1 0 0] [1 0 0] [1 0 0] [1 0 0] sum(cons(0(),x),y) = [0 0 0]x + [0 1 0]y >= [0 0 0]x + [0 1 0]y = sum(x,y) [1 0 0] [1 1 1] [1 0 0] [1 1 1] [1 0 0] [1] sum(nil(),y) = [0 1 0]y + [0] >= y = y [1 1 1] [1] [1 0 1] [1 0 1] [2 1 1] [1 0 1] [1 0 1] [2 0 1] weight(cons(n,cons(m,x))) = [0 0 0]m + [0 0 0]n + [0 0 0]x >= [0 0 0]m + [0 0 0]n + [0 0 0]x = weight(sum(cons(n,cons(m,x)),cons(0(),x))) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] problem: sum(cons(s(n),x),cons(m,y)) -> sum(cons(n,x),cons(s(m),y)) sum(cons(0(),x),y) -> sum(x,y) weight(cons(n,cons(m,x))) -> weight(sum(cons(n,cons(m,x)),cons(0(),x))) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 1 0] [0] [cons](x0, x1) = [1 1 1]x0 + [1 1 0]x1 + [0] [1 0 0] [0 1 0] [1], [1] [0] = [1] [1], [1 0 1] [0] [weight](x0) = [0 0 1]x0 + [1] [0 0 0] [0], [1 0 0] [s](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [0] [sum](x0, x1) = [1 0 0]x0 + [0 0 1]x1 + [1] [0 0 0] [0 0 0] [0] orientation: [1 0 0] [1 0 0] [1 1 0] [1 1 0] [0] [1 0 0] [1 0 0] [1 1 0] [1 1 0] [0] sum(cons(s(n),x),cons(m,y)) = [1 0 0]m + [1 0 0]n + [1 1 0]x + [0 1 0]y + [2] >= [1 0 0]m + [1 0 0]n + [1 1 0]x + [0 1 0]y + [2] = sum(cons(n,x),cons(s(m),y)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0] [1 1 0] [1 0 0] [1] [1 0 0] [1 0 0] [0] sum(cons(0(),x),y) = [1 1 0]x + [0 0 1]y + [2] >= [1 0 0]x + [0 0 1]y + [1] = sum(x,y) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [3 2 2] [2 0 0] [3 3 0] [1] [2 1 1] [1 0 0] [3 3 0] [1] weight(cons(n,cons(m,x))) = [1 1 1]m + [1 0 0]n + [1 1 0]x + [2] >= [0 0 0]m + [0 0 0]n + [0 0 0]x + [1] = weight(sum(cons(n,cons(m,x)),cons(0(),x))) [0 0 0] [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0 0 0] [0] problem: sum(cons(s(n),x),cons(m,y)) -> sum(cons(n,x),cons(s(m),y)) weight(cons(n,cons(m,x))) -> weight(sum(cons(n,cons(m,x)),cons(0(),x))) Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [1 0 0] [0] [cons](x0, x1) = [0 0 0]x0 + [1 0 1]x1 + [0] [0 0 0] [1 0 1] [1], [0] [0] = [0] [0], [1 1 0] [0] [weight](x0) = [0 0 0]x0 + [1] [1 1 0] [0], [1 0 0] [1] [s](x0) = [0 0 0]x0 + [0] [0 0 1] [1], [1 0 0] [1 1 0] [sum](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [1 0 0] [0 1 0] orientation: [1 0 1] [1 0 1] [1 0 0] [2 0 1] [2] [1 0 1] [1 0 1] [1 0 0] [2 0 1] [2] sum(cons(s(n),x),cons(m,y)) = [0 0 0]m + [0 0 0]n + [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]m + [0 0 0]n + [0 0 0]x + [0 0 0]y + [0] = sum(cons(n,x),cons(s(m),y)) [0 0 0] [1 0 1] [1 0 0] [1 0 1] [2] [0 0 0] [1 0 1] [1 0 0] [1 0 1] [0] [2 0 2] [1 0 1] [3 0 1] [1] [1 0 1] [1 0 1] [3 0 1] [0] weight(cons(n,cons(m,x))) = [0 0 0]m + [0 0 0]n + [0 0 0]x + [1] >= [0 0 0]m + [0 0 0]n + [0 0 0]x + [1] = weight(sum(cons(n,cons(m,x)),cons(0(),x))) [2 0 2] [1 0 1] [3 0 1] [1] [1 0 1] [1 0 1] [3 0 1] [0] problem: sum(cons(s(n),x),cons(m,y)) -> sum(cons(n,x),cons(s(m),y)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 1 0] [cons](x0, x1) = [1 0 0]x0 + [0 0 0]x1 [0 0 1] [0 0 0] , [1 0 0] [0] [s](x0) = [0 0 0]x0 + [0] [0 0 1] [1], [1 0 1] [1 0 0] [sum](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 1 1] [0 0 0] orientation: [1 0 0] [1 0 1] [1 1 0] [1 1 0] [1] [1 0 0] [1 0 1] [1 1 0] [1 1 0] sum(cons(s(n),x),cons(m,y)) = [0 0 0]m + [0 0 0]n + [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]m + [0 0 0]n + [0 0 0]x + [0 0 0]y = sum(cons(n,x),cons(s(m),y)) [0 0 0] [1 0 1] [0 0 0] [0 0 0] [1] [0 0 0] [1 0 1] [0 0 0] [0 0 0] problem: Qed