6.30/1.90 YES 6.30/1.91 6.30/1.91 Problem: 6.30/1.91 strict: 6.30/1.91 n(s(x1)) -> s(x1) 6.30/1.91 o(s(x1)) -> s(x1) 6.30/1.91 weak: 6.30/1.91 t(x1) -> t(c(n(x1))) 6.30/1.91 c(n(x1)) -> n(c(x1)) 6.30/1.91 c(o(x1)) -> o(c(x1)) 6.30/1.91 c(o(x1)) -> o(x1) 6.30/1.91 6.30/1.91 Proof: 6.30/1.91 Arctic Interpretation Processor: 6.30/1.91 dimension: 2 6.30/1.91 interpretation: 6.30/1.91 [0 -&] 6.30/1.91 [c](x0) = [0 0 ]x0, 6.30/1.91 6.30/1.91 [0 0 ] 6.30/1.91 [t](x0) = [-& -&]x0, 6.30/1.91 6.30/1.91 [1 1] 6.30/1.91 [o](x0) = [4 4]x0, 6.30/1.91 6.30/1.91 [0 0 ] 6.30/1.91 [n](x0) = [0 -&]x0, 6.30/1.91 6.30/1.91 [1 0] 6.30/1.91 [s](x0) = [0 0]x0 6.30/1.91 orientation: 6.30/1.91 [1 0] [1 0] 6.30/1.91 n(s(x1)) = [1 0]x1 >= [0 0]x1 = s(x1) 6.30/1.91 6.30/1.91 [2 1] [1 0] 6.30/1.91 o(s(x1)) = [5 4]x1 >= [0 0]x1 = s(x1) 6.30/1.91 6.30/1.91 [0 0 ] [0 0 ] 6.30/1.91 t(x1) = [-& -&]x1 >= [-& -&]x1 = t(c(n(x1))) 6.30/1.91 6.30/1.91 [0 0] [0 0 ] 6.30/1.91 c(n(x1)) = [0 0]x1 >= [0 -&]x1 = n(c(x1)) 6.30/1.91 6.30/1.91 [1 1] [1 1] 6.30/1.91 c(o(x1)) = [4 4]x1 >= [4 4]x1 = o(c(x1)) 6.30/1.91 6.30/1.91 [1 1] [1 1] 6.30/1.91 c(o(x1)) = [4 4]x1 >= [4 4]x1 = o(x1) 6.30/1.91 problem: 6.30/1.91 strict: 6.30/1.91 n(s(x1)) -> s(x1) 6.30/1.91 weak: 6.30/1.91 t(x1) -> t(c(n(x1))) 6.30/1.91 c(n(x1)) -> n(c(x1)) 6.30/1.91 c(o(x1)) -> o(c(x1)) 6.30/1.91 c(o(x1)) -> o(x1) 6.30/1.91 String Reversal Processor: 6.30/1.91 strict: 6.30/1.91 s(n(x1)) -> s(x1) 6.30/1.91 weak: 6.30/1.91 t(x1) -> n(c(t(x1))) 6.30/1.91 n(c(x1)) -> c(n(x1)) 6.30/1.91 o(c(x1)) -> c(o(x1)) 6.30/1.91 o(c(x1)) -> o(x1) 6.30/1.91 Matrix Interpretation Processor: dim=2 6.30/1.91 6.30/1.91 interpretation: 6.30/1.91 [1 0] 6.30/1.91 [c](x0) = [0 0]x0, 6.30/1.91 6.30/1.91 [1 2] [0] 6.30/1.91 [t](x0) = [0 0]x0 + [1], 6.30/1.91 6.30/1.91 [2 0] 6.30/1.91 [o](x0) = [0 0]x0, 6.30/1.91 6.30/1.91 [0] 6.30/1.91 [n](x0) = x0 + [1], 6.30/1.91 6.30/1.91 [1 1] [0] 6.30/1.91 [s](x0) = [2 0]x0 + [1] 6.30/1.91 orientation: 6.30/1.91 [1 1] [1] [1 1] [0] 6.30/1.91 s(n(x1)) = [2 0]x1 + [1] >= [2 0]x1 + [1] = s(x1) 6.30/1.91 6.30/1.91 [1 2] [0] [1 2] [0] 6.30/1.91 t(x1) = [0 0]x1 + [1] >= [0 0]x1 + [1] = n(c(t(x1))) 6.30/1.91 6.30/1.91 [1 0] [0] [1 0] 6.30/1.91 n(c(x1)) = [0 0]x1 + [1] >= [0 0]x1 = c(n(x1)) 6.30/1.91 6.30/1.91 [2 0] [2 0] 6.30/1.91 o(c(x1)) = [0 0]x1 >= [0 0]x1 = c(o(x1)) 6.30/1.91 6.30/1.91 [2 0] [2 0] 6.30/1.91 o(c(x1)) = [0 0]x1 >= [0 0]x1 = o(x1) 6.30/1.91 problem: 6.30/1.91 strict: 6.30/1.91 6.30/1.91 weak: 6.30/1.91 t(x1) -> n(c(t(x1))) 6.30/1.91 n(c(x1)) -> c(n(x1)) 6.30/1.91 o(c(x1)) -> c(o(x1)) 6.30/1.91 o(c(x1)) -> o(x1) 6.30/1.91 Qed 6.30/1.91 EOF