10.59/3.07 YES 10.59/3.08 10.59/3.08 Problem: 10.59/3.08 strict: 10.59/3.08 a(c(b(x1))) -> b(a(b(a(x1)))) 10.59/3.08 a(a(x1)) -> a(b(a(x1))) 10.59/3.08 weak: 10.59/3.08 b(x1) -> b(c(x1)) 10.59/3.08 10.59/3.08 Proof: 10.59/3.08 Bounds Processor: 10.59/3.08 bound: 2 10.59/3.08 enrichment: match-rt 10.59/3.08 automaton: 10.59/3.08 final states: {4} 10.59/3.08 transitions: 10.59/3.08 b1(11) -> 12* 10.59/3.08 b1(13) -> 14* 10.59/3.08 a1(10) -> 11* 10.59/3.08 a1(132) -> 133* 10.59/3.08 a1(27) -> 28* 10.59/3.08 a1(12) -> 13* 10.59/3.08 a2(60) -> 61* 10.59/3.08 a2(124) -> 125* 10.59/3.08 a2(94) -> 95* 10.59/3.08 a2(96) -> 97* 10.59/3.08 a2(58) -> 59* 10.59/3.08 b2(139) -> 140* 10.59/3.08 b2(59) -> 60* 10.59/3.08 b2(61) -> 62* 10.59/3.08 b2(118) -> 119* 10.59/3.08 b2(95) -> 96* 10.59/3.08 a0(4) -> 4* 10.59/3.08 c1(87) -> 88* 10.59/3.08 c1(47) -> 48* 10.59/3.08 c1(54) -> 55* 10.59/3.08 c0(4) -> 4* 10.59/3.08 c2(152) -> 153* 10.59/3.08 c2(117) -> 118* 10.59/3.08 c2(107) -> 108* 10.59/3.08 c2(164) -> 165* 10.59/3.08 c2(171) -> 172* 10.59/3.08 c2(158) -> 159* 10.59/3.08 c2(138) -> 139* 10.59/3.08 b0(4) -> 4* 10.59/3.08 4 -> 54,10 10.59/3.08 11 -> 138,87,28 10.59/3.08 12 -> 94,59 10.59/3.08 13 -> 117,58,47,11,4,27 10.59/3.08 14 -> 11,4 10.59/3.08 28 -> 11* 10.59/3.08 48 -> 13* 10.59/3.08 55 -> 13* 10.59/3.08 59 -> 152* 10.59/3.08 61 -> 107* 10.59/3.08 62 -> 59,28 10.59/3.08 88 -> 11* 10.59/3.08 95 -> 164* 10.59/3.08 97 -> 59,11 10.59/3.08 108 -> 61* 10.59/3.08 118 -> 158,132,124 10.59/3.08 119 -> 14* 10.59/3.08 125 -> 59* 10.59/3.08 133 -> 11* 10.59/3.08 139 -> 171* 10.59/3.08 140 -> 12* 10.59/3.08 153 -> 59* 10.59/3.08 159 -> 118* 10.59/3.08 165 -> 95* 10.59/3.08 172 -> 139* 10.59/3.08 problem: 10.59/3.08 strict: 10.59/3.08 a(a(x1)) -> a(b(a(x1))) 10.59/3.08 weak: 10.59/3.08 b(x1) -> b(c(x1)) 10.59/3.08 String Reversal Processor: 10.59/3.08 strict: 10.59/3.08 a(a(x1)) -> a(b(a(x1))) 10.59/3.08 weak: 10.59/3.08 b(x1) -> c(b(x1)) 10.59/3.08 Arctic Interpretation Processor: 10.59/3.08 dimension: 2 10.59/3.08 interpretation: 10.59/3.08 [1 2] 10.59/3.08 [a](x0) = [3 5]x0, 10.59/3.08 10.59/3.08 [0 0 ] 10.59/3.08 [c](x0) = [-& -&]x0, 10.59/3.08 10.59/3.08 [0 0 ] 10.59/3.08 [b](x0) = [0 -&]x0 10.59/3.08 orientation: 10.59/3.08 [5 7 ] [4 6] 10.59/3.08 a(a(x1)) = [8 10]x1 >= [6 8]x1 = a(b(a(x1))) 10.59/3.08 10.59/3.08 [0 0 ] [0 0 ] 10.59/3.08 b(x1) = [0 -&]x1 >= [-& -&]x1 = c(b(x1)) 10.59/3.08 problem: 10.59/3.08 strict: 10.59/3.08 10.59/3.08 weak: 10.59/3.08 b(x1) -> c(b(x1)) 10.59/3.08 Qed 10.59/3.08 EOF