176.89/45.22 YES 176.89/45.23 176.89/45.23 Problem: 176.89/45.23 a(a(x1)) -> a(b(x1)) 176.89/45.23 a(c(x1)) -> b(x1) 176.89/45.23 b(b(x1)) -> c(b(a(x1))) 176.89/45.23 176.89/45.23 Proof: 176.89/45.23 String Reversal Processor: 176.89/45.23 a(a(x1)) -> b(a(x1)) 176.89/45.23 c(a(x1)) -> b(x1) 176.89/45.23 b(b(x1)) -> a(b(c(x1))) 176.89/45.23 DP Processor: 176.89/45.23 DPs: 176.89/45.23 a#(a(x1)) -> b#(a(x1)) 176.89/45.23 c#(a(x1)) -> b#(x1) 176.89/45.23 b#(b(x1)) -> c#(x1) 176.89/45.23 b#(b(x1)) -> b#(c(x1)) 176.89/45.23 b#(b(x1)) -> a#(b(c(x1))) 176.89/45.23 TRS: 176.89/45.23 a(a(x1)) -> b(a(x1)) 176.89/45.23 c(a(x1)) -> b(x1) 176.89/45.23 b(b(x1)) -> a(b(c(x1))) 176.89/45.23 TDG Processor: 176.89/45.23 DPs: 176.89/45.23 a#(a(x1)) -> b#(a(x1)) 176.89/45.23 c#(a(x1)) -> b#(x1) 176.89/45.23 b#(b(x1)) -> c#(x1) 176.89/45.23 b#(b(x1)) -> b#(c(x1)) 176.89/45.23 b#(b(x1)) -> a#(b(c(x1))) 176.89/45.23 TRS: 176.89/45.23 a(a(x1)) -> b(a(x1)) 176.89/45.23 c(a(x1)) -> b(x1) 176.89/45.23 b(b(x1)) -> a(b(c(x1))) 176.89/45.23 graph: 176.89/45.23 c#(a(x1)) -> b#(x1) -> b#(b(x1)) -> a#(b(c(x1))) 176.89/45.23 c#(a(x1)) -> b#(x1) -> b#(b(x1)) -> b#(c(x1)) 176.89/45.23 c#(a(x1)) -> b#(x1) -> b#(b(x1)) -> c#(x1) 176.89/45.23 b#(b(x1)) -> c#(x1) -> c#(a(x1)) -> b#(x1) 176.89/45.23 b#(b(x1)) -> b#(c(x1)) -> b#(b(x1)) -> a#(b(c(x1))) 176.89/45.23 b#(b(x1)) -> b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) 176.89/45.23 b#(b(x1)) -> b#(c(x1)) -> b#(b(x1)) -> c#(x1) 176.89/45.23 b#(b(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(a(x1)) 176.89/45.23 a#(a(x1)) -> b#(a(x1)) -> b#(b(x1)) -> a#(b(c(x1))) 176.89/45.23 a#(a(x1)) -> b#(a(x1)) -> b#(b(x1)) -> b#(c(x1)) 176.89/45.23 a#(a(x1)) -> b#(a(x1)) -> b#(b(x1)) -> c#(x1) 176.89/45.23 Arctic Interpretation Processor: 176.89/45.23 dimension: 1 176.89/45.23 usable rules: 176.89/45.23 a(a(x1)) -> b(a(x1)) 176.89/45.23 c(a(x1)) -> b(x1) 176.89/45.23 b(b(x1)) -> a(b(c(x1))) 176.89/45.23 interpretation: 176.89/45.23 [c#](x0) = x0, 176.89/45.23 176.89/45.23 [b#](x0) = x0, 176.89/45.23 176.89/45.23 [a#](x0) = x0 + 0, 176.89/45.23 176.89/45.23 [c](x0) = x0 + 0, 176.89/45.23 176.89/45.23 [b](x0) = 1x0 + 3, 176.89/45.23 176.89/45.23 [a](x0) = 1x0 + 3 176.89/45.23 orientation: 176.89/45.23 a#(a(x1)) = 1x1 + 3 >= 1x1 + 3 = b#(a(x1)) 176.89/45.23 176.89/45.23 c#(a(x1)) = 1x1 + 3 >= x1 = b#(x1) 176.89/45.23 176.89/45.23 b#(b(x1)) = 1x1 + 3 >= x1 = c#(x1) 176.89/45.23 176.89/45.23 b#(b(x1)) = 1x1 + 3 >= x1 + 0 = b#(c(x1)) 176.89/45.23 176.89/45.23 b#(b(x1)) = 1x1 + 3 >= 1x1 + 3 = a#(b(c(x1))) 176.89/45.23 176.89/45.23 a(a(x1)) = 2x1 + 4 >= 2x1 + 4 = b(a(x1)) 176.89/45.23 176.89/45.23 c(a(x1)) = 1x1 + 3 >= 1x1 + 3 = b(x1) 176.89/45.23 176.89/45.23 b(b(x1)) = 2x1 + 4 >= 2x1 + 4 = a(b(c(x1))) 176.89/45.23 problem: 176.89/45.23 DPs: 176.89/45.23 a#(a(x1)) -> b#(a(x1)) 176.89/45.23 b#(b(x1)) -> a#(b(c(x1))) 176.89/45.23 TRS: 176.89/45.23 a(a(x1)) -> b(a(x1)) 176.89/45.23 c(a(x1)) -> b(x1) 176.89/45.23 b(b(x1)) -> a(b(c(x1))) 176.89/45.23 Restore Modifier: 176.89/45.23 DPs: 176.89/45.23 a#(a(x1)) -> b#(a(x1)) 176.89/45.23 b#(b(x1)) -> a#(b(c(x1))) 176.89/45.23 TRS: 176.89/45.23 a(a(x1)) -> b(a(x1)) 176.89/45.23 c(a(x1)) -> b(x1) 176.89/45.23 b(b(x1)) -> a(b(c(x1))) 176.89/45.23 EDG Processor: 176.89/45.23 DPs: 176.89/45.23 a#(a(x1)) -> b#(a(x1)) 176.89/45.23 b#(b(x1)) -> a#(b(c(x1))) 176.89/45.23 TRS: 176.89/45.23 a(a(x1)) -> b(a(x1)) 176.89/45.23 c(a(x1)) -> b(x1) 176.89/45.23 b(b(x1)) -> a(b(c(x1))) 176.89/45.23 graph: 176.89/45.23 b#(b(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(a(x1)) 176.89/45.23 a#(a(x1)) -> b#(a(x1)) -> b#(b(x1)) -> a#(b(c(x1))) 176.89/45.23 Arctic Interpretation Processor: 176.89/45.23 dimension: 2 176.89/45.23 usable rules: 176.89/45.23 a(a(x1)) -> b(a(x1)) 176.89/45.23 c(a(x1)) -> b(x1) 176.89/45.23 b(b(x1)) -> a(b(c(x1))) 176.89/45.23 interpretation: 176.89/45.23 [b#](x0) = [0 0]x0 + [0], 176.89/45.23 176.89/45.23 [a#](x0) = [2 0]x0 + [0], 176.89/45.23 176.89/45.23 [0 -&] [0 ] 176.89/45.23 [c](x0) = [0 -&]x0 + [-&], 176.89/45.23 176.89/45.23 [0 0] [0] 176.89/45.23 [b](x0) = [2 0]x0 + [3], 176.89/45.23 176.89/45.23 [2 0] [3] 176.89/45.23 [a](x0) = [2 0]x0 + [0] 176.89/45.23 orientation: 176.89/45.23 a#(a(x1)) = [4 2]x1 + [5] >= [2 0]x1 + [3] = b#(a(x1)) 176.89/45.23 176.89/45.23 b#(b(x1)) = [2 0]x1 + [3] >= [2 -&]x1 + [3] = a#(b(c(x1))) 176.89/45.23 176.89/45.23 [4 2] [5] [2 0] [3] 176.89/45.23 a(a(x1)) = [4 2]x1 + [5] >= [4 2]x1 + [5] = b(a(x1)) 176.89/45.23 176.89/45.23 [2 0] [3] [0 0] [0] 176.89/45.23 c(a(x1)) = [2 0]x1 + [3] >= [2 0]x1 + [3] = b(x1) 176.89/45.23 176.89/45.23 [2 0] [3] [2 -&] [3] 176.89/45.23 b(b(x1)) = [2 2]x1 + [3] >= [2 -&]x1 + [3] = a(b(c(x1))) 176.89/45.23 problem: 176.89/45.23 DPs: 176.89/45.23 b#(b(x1)) -> a#(b(c(x1))) 176.89/45.23 TRS: 176.89/45.23 a(a(x1)) -> b(a(x1)) 176.89/45.23 c(a(x1)) -> b(x1) 176.89/45.23 b(b(x1)) -> a(b(c(x1))) 176.89/45.23 Restore Modifier: 176.89/45.23 DPs: 176.89/45.23 b#(b(x1)) -> a#(b(c(x1))) 176.89/45.23 TRS: 176.89/45.23 a(a(x1)) -> b(a(x1)) 176.89/45.23 c(a(x1)) -> b(x1) 176.89/45.23 b(b(x1)) -> a(b(c(x1))) 176.89/45.23 EDG Processor: 176.89/45.23 DPs: 176.89/45.23 b#(b(x1)) -> a#(b(c(x1))) 176.89/45.23 TRS: 176.89/45.23 a(a(x1)) -> b(a(x1)) 176.89/45.23 c(a(x1)) -> b(x1) 176.89/45.23 b(b(x1)) -> a(b(c(x1))) 176.89/45.23 graph: 176.89/45.23 176.89/45.23 SCC Processor: 176.89/45.23 #sccs: 0 176.89/45.23 #rules: 0 176.89/45.23 #arcs: 0/1 176.89/45.23 176.89/45.24 EOF