172.47/44.00 YES 172.54/44.00 172.54/44.00 Problem: 172.54/44.00 a(x1) -> b(b(c(x1))) 172.54/44.00 c(b(b(x1))) -> a(b(c(x1))) 172.54/44.00 c(c(x1)) -> x1 172.54/44.00 172.54/44.00 Proof: 172.54/44.00 String Reversal Processor: 172.54/44.00 a(x1) -> c(b(b(x1))) 172.54/44.00 b(b(c(x1))) -> c(b(a(x1))) 172.54/44.00 c(c(x1)) -> x1 172.54/44.00 DP Processor: 172.54/44.00 DPs: 172.54/44.00 a#(x1) -> b#(x1) 172.54/44.00 a#(x1) -> b#(b(x1)) 172.54/44.00 a#(x1) -> c#(b(b(x1))) 172.54/44.00 b#(b(c(x1))) -> a#(x1) 172.54/44.00 b#(b(c(x1))) -> b#(a(x1)) 172.54/44.00 b#(b(c(x1))) -> c#(b(a(x1))) 172.54/44.00 TRS: 172.54/44.00 a(x1) -> c(b(b(x1))) 172.54/44.00 b(b(c(x1))) -> c(b(a(x1))) 172.54/44.00 c(c(x1)) -> x1 172.54/44.00 TDG Processor: 172.54/44.00 DPs: 172.54/44.00 a#(x1) -> b#(x1) 172.54/44.00 a#(x1) -> b#(b(x1)) 172.54/44.00 a#(x1) -> c#(b(b(x1))) 172.54/44.00 b#(b(c(x1))) -> a#(x1) 172.54/44.00 b#(b(c(x1))) -> b#(a(x1)) 172.54/44.00 b#(b(c(x1))) -> c#(b(a(x1))) 172.54/44.00 TRS: 172.54/44.00 a(x1) -> c(b(b(x1))) 172.54/44.00 b(b(c(x1))) -> c(b(a(x1))) 172.54/44.00 c(c(x1)) -> x1 172.54/44.00 graph: 172.54/44.00 b#(b(c(x1))) -> b#(a(x1)) -> b#(b(c(x1))) -> c#(b(a(x1))) 172.54/44.00 b#(b(c(x1))) -> b#(a(x1)) -> b#(b(c(x1))) -> b#(a(x1)) 172.54/44.00 b#(b(c(x1))) -> b#(a(x1)) -> b#(b(c(x1))) -> a#(x1) 172.54/44.00 b#(b(c(x1))) -> a#(x1) -> a#(x1) -> c#(b(b(x1))) 172.54/44.00 b#(b(c(x1))) -> a#(x1) -> a#(x1) -> b#(b(x1)) 172.54/44.00 b#(b(c(x1))) -> a#(x1) -> a#(x1) -> b#(x1) 172.54/44.00 a#(x1) -> b#(b(x1)) -> b#(b(c(x1))) -> c#(b(a(x1))) 172.54/44.00 a#(x1) -> b#(b(x1)) -> b#(b(c(x1))) -> b#(a(x1)) 172.54/44.00 a#(x1) -> b#(b(x1)) -> b#(b(c(x1))) -> a#(x1) 172.54/44.00 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> c#(b(a(x1))) 172.54/44.00 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> b#(a(x1)) 172.54/44.00 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> a#(x1) 172.54/44.00 SCC Processor: 172.54/44.00 #sccs: 1 172.54/44.00 #rules: 4 172.54/44.00 #arcs: 12/36 172.54/44.00 DPs: 172.54/44.00 b#(b(c(x1))) -> b#(a(x1)) 172.54/44.00 b#(b(c(x1))) -> a#(x1) 172.54/44.00 a#(x1) -> b#(x1) 172.54/44.00 a#(x1) -> b#(b(x1)) 172.54/44.00 TRS: 172.54/44.00 a(x1) -> c(b(b(x1))) 172.54/44.00 b(b(c(x1))) -> c(b(a(x1))) 172.54/44.00 c(c(x1)) -> x1 172.54/44.00 Arctic Interpretation Processor: 172.54/44.00 dimension: 2 172.54/44.00 usable rules: 172.54/44.00 a(x1) -> c(b(b(x1))) 172.54/44.00 b(b(c(x1))) -> c(b(a(x1))) 172.54/44.00 c(c(x1)) -> x1 172.54/44.00 interpretation: 172.54/44.00 [b#](x0) = [2 0]x0 + [0], 172.54/44.00 172.54/44.00 [a#](x0) = [2 3]x0 + [3], 172.54/44.00 172.54/44.00 [-& 0 ] [0] 172.54/44.00 [b](x0) = [0 -&]x0 + [0], 172.54/44.00 172.54/44.00 [-& 0 ] [0] 172.54/44.00 [c](x0) = [0 2 ]x0 + [2], 172.54/44.00 172.54/44.00 [-& 0 ] [0] 172.54/44.00 [a](x0) = [0 2 ]x0 + [2] 172.54/44.00 orientation: 172.54/44.00 b#(b(c(x1))) = [2 4]x1 + [4] >= [0 2]x1 + [2] = b#(a(x1)) 172.54/44.00 172.54/44.00 b#(b(c(x1))) = [2 4]x1 + [4] >= [2 3]x1 + [3] = a#(x1) 172.54/44.00 172.54/44.00 a#(x1) = [2 3]x1 + [3] >= [2 0]x1 + [0] = b#(x1) 172.54/44.00 172.54/44.00 a#(x1) = [2 3]x1 + [3] >= [0 2]x1 + [2] = b#(b(x1)) 172.54/44.00 172.54/44.00 [-& 0 ] [0] [-& 0 ] [0] 172.54/44.00 a(x1) = [0 2 ]x1 + [2] >= [0 2 ]x1 + [2] = c(b(b(x1))) 172.54/44.00 172.54/44.00 [-& 0 ] [0] [-& 0 ] [0] 172.54/44.00 b(b(c(x1))) = [0 2 ]x1 + [2] >= [0 2 ]x1 + [2] = c(b(a(x1))) 172.54/44.00 172.54/44.00 [0 2] [2] 172.54/44.00 c(c(x1)) = [2 4]x1 + [4] >= x1 = x1 172.54/44.00 problem: 172.54/44.00 DPs: 172.54/44.00 b#(b(c(x1))) -> a#(x1) 172.54/44.00 a#(x1) -> b#(x1) 172.54/44.00 TRS: 172.54/44.00 a(x1) -> c(b(b(x1))) 172.54/44.00 b(b(c(x1))) -> c(b(a(x1))) 172.54/44.00 c(c(x1)) -> x1 172.54/44.00 Restore Modifier: 172.54/44.00 DPs: 172.54/44.00 b#(b(c(x1))) -> a#(x1) 172.54/44.00 a#(x1) -> b#(x1) 172.54/44.00 TRS: 172.54/44.00 a(x1) -> c(b(b(x1))) 172.54/44.00 b(b(c(x1))) -> c(b(a(x1))) 172.54/44.00 c(c(x1)) -> x1 172.54/44.00 EDG Processor: 172.54/44.00 DPs: 172.54/44.00 b#(b(c(x1))) -> a#(x1) 172.54/44.00 a#(x1) -> b#(x1) 172.54/44.00 TRS: 172.54/44.00 a(x1) -> c(b(b(x1))) 172.54/44.00 b(b(c(x1))) -> c(b(a(x1))) 172.54/44.00 c(c(x1)) -> x1 172.54/44.00 graph: 172.54/44.00 b#(b(c(x1))) -> a#(x1) -> a#(x1) -> b#(x1) 172.54/44.00 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> a#(x1) 172.54/44.00 Usable Rule Processor: 172.54/44.00 DPs: 172.54/44.00 b#(b(c(x1))) -> a#(x1) 172.54/44.00 a#(x1) -> b#(x1) 172.54/44.00 TRS: 172.54/44.00 172.54/44.00 Arctic Interpretation Processor: 172.54/44.00 dimension: 1 172.54/44.00 usable rules: 172.54/44.00 172.54/44.00 interpretation: 172.54/44.00 [b#](x0) = x0, 172.54/44.00 172.54/44.00 [a#](x0) = x0, 172.54/44.00 172.54/44.00 [b](x0) = x0, 172.54/44.00 172.54/44.00 [c](x0) = 1x0 172.54/44.00 orientation: 172.54/44.00 b#(b(c(x1))) = 1x1 >= x1 = a#(x1) 172.54/44.00 172.54/44.00 a#(x1) = x1 >= x1 = b#(x1) 172.54/44.00 problem: 172.54/44.00 DPs: 172.54/44.00 a#(x1) -> b#(x1) 172.54/44.00 TRS: 172.54/44.00 172.54/44.00 Restore Modifier: 172.54/44.00 DPs: 172.54/44.00 a#(x1) -> b#(x1) 172.54/44.00 TRS: 172.54/44.00 a(x1) -> c(b(b(x1))) 172.54/44.00 b(b(c(x1))) -> c(b(a(x1))) 172.54/44.00 c(c(x1)) -> x1 172.54/44.00 EDG Processor: 172.54/44.00 DPs: 172.54/44.00 a#(x1) -> b#(x1) 172.54/44.00 TRS: 172.54/44.00 a(x1) -> c(b(b(x1))) 172.54/44.00 b(b(c(x1))) -> c(b(a(x1))) 172.54/44.00 c(c(x1)) -> x1 172.54/44.00 graph: 172.54/44.00 172.54/44.00 SCC Processor: 172.54/44.00 #sccs: 0 172.54/44.00 #rules: 0 172.54/44.00 #arcs: 0/1 172.54/44.00 172.54/44.01 EOF