187.21/47.72 YES 187.21/47.73 187.21/47.73 Problem: 187.21/47.73 a(x1) -> b(b(c(b(c(x1))))) 187.21/47.73 c(b(b(x1))) -> a(x1) 187.21/47.73 c(c(x1)) -> x1 187.21/47.73 187.21/47.73 Proof: 187.21/47.73 String Reversal Processor: 187.21/47.73 a(x1) -> c(b(c(b(b(x1))))) 187.21/47.73 b(b(c(x1))) -> a(x1) 187.21/47.73 c(c(x1)) -> x1 187.21/47.73 DP Processor: 187.21/47.73 DPs: 187.21/47.73 a#(x1) -> b#(x1) 187.21/47.73 a#(x1) -> b#(b(x1)) 187.21/47.73 a#(x1) -> c#(b(b(x1))) 187.21/47.73 a#(x1) -> b#(c(b(b(x1)))) 187.21/47.73 a#(x1) -> c#(b(c(b(b(x1))))) 187.21/47.73 b#(b(c(x1))) -> a#(x1) 187.21/47.73 TRS: 187.21/47.73 a(x1) -> c(b(c(b(b(x1))))) 187.21/47.73 b(b(c(x1))) -> a(x1) 187.21/47.73 c(c(x1)) -> x1 187.21/47.73 TDG Processor: 187.21/47.73 DPs: 187.21/47.73 a#(x1) -> b#(x1) 187.21/47.73 a#(x1) -> b#(b(x1)) 187.21/47.73 a#(x1) -> c#(b(b(x1))) 187.21/47.73 a#(x1) -> b#(c(b(b(x1)))) 187.21/47.73 a#(x1) -> c#(b(c(b(b(x1))))) 187.21/47.73 b#(b(c(x1))) -> a#(x1) 187.21/47.73 TRS: 187.21/47.73 a(x1) -> c(b(c(b(b(x1))))) 187.21/47.73 b(b(c(x1))) -> a(x1) 187.21/47.73 c(c(x1)) -> x1 187.21/47.73 graph: 187.21/47.73 b#(b(c(x1))) -> a#(x1) -> a#(x1) -> c#(b(c(b(b(x1))))) 187.21/47.73 b#(b(c(x1))) -> a#(x1) -> a#(x1) -> b#(c(b(b(x1)))) 187.21/47.73 b#(b(c(x1))) -> a#(x1) -> a#(x1) -> c#(b(b(x1))) 187.21/47.73 b#(b(c(x1))) -> a#(x1) -> a#(x1) -> b#(b(x1)) 187.21/47.73 b#(b(c(x1))) -> a#(x1) -> a#(x1) -> b#(x1) 187.21/47.73 a#(x1) -> b#(b(x1)) -> b#(b(c(x1))) -> a#(x1) 187.21/47.73 a#(x1) -> b#(c(b(b(x1)))) -> b#(b(c(x1))) -> a#(x1) 187.21/47.73 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> a#(x1) 187.21/47.73 SCC Processor: 187.21/47.73 #sccs: 1 187.21/47.73 #rules: 4 187.21/47.73 #arcs: 8/36 187.21/47.73 DPs: 187.21/47.73 b#(b(c(x1))) -> a#(x1) 187.21/47.73 a#(x1) -> b#(x1) 187.21/47.73 a#(x1) -> b#(b(x1)) 187.21/47.73 a#(x1) -> b#(c(b(b(x1)))) 187.21/47.73 TRS: 187.21/47.73 a(x1) -> c(b(c(b(b(x1))))) 187.21/47.73 b(b(c(x1))) -> a(x1) 187.21/47.73 c(c(x1)) -> x1 187.21/47.73 Arctic Interpretation Processor: 187.21/47.73 dimension: 2 187.21/47.73 usable rules: 187.21/47.73 a(x1) -> c(b(c(b(b(x1))))) 187.21/47.73 b(b(c(x1))) -> a(x1) 187.21/47.73 c(c(x1)) -> x1 187.21/47.73 interpretation: 187.21/47.73 [b#](x0) = [2 1]x0 + [0], 187.21/47.73 187.21/47.73 [a#](x0) = [2 3]x0 + [3], 187.21/47.73 187.21/47.73 [-& 0 ] [0] 187.21/47.73 [b](x0) = [0 -&]x0 + [1], 187.21/47.73 187.21/47.73 [-& 0 ] [0] 187.21/47.73 [c](x0) = [0 1 ]x0 + [2], 187.21/47.73 187.21/47.73 [-& 0 ] [1] 187.21/47.73 [a](x0) = [0 1 ]x0 + [2] 187.21/47.73 orientation: 187.21/47.73 b#(b(c(x1))) = [2 3]x1 + [4] >= [2 3]x1 + [3] = a#(x1) 187.21/47.73 187.21/47.73 a#(x1) = [2 3]x1 + [3] >= [2 1]x1 + [0] = b#(x1) 187.21/47.73 187.21/47.73 a#(x1) = [2 3]x1 + [3] >= [1 2]x1 + [2] = b#(b(x1)) 187.21/47.73 187.21/47.73 a#(x1) = [2 3]x1 + [3] >= [1 2]x1 + [3] = b#(c(b(b(x1)))) 187.21/47.73 187.21/47.73 [-& 0 ] [1] [-& 0 ] [1] 187.21/47.73 a(x1) = [0 1 ]x1 + [2] >= [0 1 ]x1 + [2] = c(b(c(b(b(x1))))) 187.21/47.73 187.21/47.73 [-& 0 ] [1] [-& 0 ] [1] 187.21/47.73 b(b(c(x1))) = [0 1 ]x1 + [2] >= [0 1 ]x1 + [2] = a(x1) 187.21/47.73 187.21/47.73 [0 1] [2] 187.21/47.73 c(c(x1)) = [1 2]x1 + [3] >= x1 = x1 187.21/47.73 problem: 187.21/47.73 DPs: 187.21/47.73 b#(b(c(x1))) -> a#(x1) 187.21/47.73 a#(x1) -> b#(x1) 187.21/47.73 a#(x1) -> b#(c(b(b(x1)))) 187.21/47.73 TRS: 187.21/47.73 a(x1) -> c(b(c(b(b(x1))))) 187.21/47.73 b(b(c(x1))) -> a(x1) 187.21/47.73 c(c(x1)) -> x1 187.21/47.73 Restore Modifier: 187.21/47.73 DPs: 187.21/47.73 b#(b(c(x1))) -> a#(x1) 187.21/47.73 a#(x1) -> b#(x1) 187.21/47.73 a#(x1) -> b#(c(b(b(x1)))) 187.21/47.73 TRS: 187.21/47.73 a(x1) -> c(b(c(b(b(x1))))) 187.21/47.73 b(b(c(x1))) -> a(x1) 187.21/47.73 c(c(x1)) -> x1 187.21/47.73 EDG Processor: 187.21/47.73 DPs: 187.21/47.73 b#(b(c(x1))) -> a#(x1) 187.21/47.73 a#(x1) -> b#(x1) 187.21/47.73 a#(x1) -> b#(c(b(b(x1)))) 187.21/47.73 TRS: 187.21/47.73 a(x1) -> c(b(c(b(b(x1))))) 187.21/47.73 b(b(c(x1))) -> a(x1) 187.21/47.73 c(c(x1)) -> x1 187.21/47.73 graph: 187.21/47.73 b#(b(c(x1))) -> a#(x1) -> a#(x1) -> b#(x1) 187.21/47.73 b#(b(c(x1))) -> a#(x1) -> a#(x1) -> b#(c(b(b(x1)))) 187.21/47.73 a#(x1) -> b#(c(b(b(x1)))) -> b#(b(c(x1))) -> a#(x1) 187.21/47.73 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> a#(x1) 187.21/47.73 Arctic Interpretation Processor: 187.21/47.73 dimension: 2 187.21/47.73 usable rules: 187.21/47.73 a(x1) -> c(b(c(b(b(x1))))) 187.21/47.73 b(b(c(x1))) -> a(x1) 187.21/47.73 c(c(x1)) -> x1 187.21/47.73 interpretation: 187.21/47.73 [b#](x0) = [0 0]x0 + [0], 187.21/47.73 187.21/47.73 [a#](x0) = [0 3]x0 + [3], 187.21/47.73 187.21/47.73 [-& 2 ] [0 ] 187.21/47.73 [b](x0) = [-2 -&]x0 + [-1], 187.21/47.73 187.21/47.73 [-& 2 ] [1] 187.21/47.73 [c](x0) = [-2 2 ]x0 + [2], 187.21/47.73 187.21/47.73 [-& 2 ] [1] 187.21/47.73 [a](x0) = [-2 2 ]x0 + [2] 187.21/47.73 orientation: 187.21/47.73 b#(b(c(x1))) = [0 4]x1 + [4] >= [0 3]x1 + [3] = a#(x1) 187.21/47.73 187.21/47.73 a#(x1) = [0 3]x1 + [3] >= [0 0]x1 + [0] = b#(x1) 187.21/47.73 187.21/47.73 a#(x1) = [0 3]x1 + [3] >= [-2 2 ]x1 + [2] = b#(c(b(b(x1)))) 187.21/47.73 187.21/47.73 [-& 2 ] [1] [-& 2 ] [1] 187.21/47.73 a(x1) = [-2 2 ]x1 + [2] >= [-2 2 ]x1 + [2] = c(b(c(b(b(x1))))) 187.21/47.73 187.21/47.73 [-& 2 ] [1] [-& 2 ] [1] 187.21/47.73 b(b(c(x1))) = [-2 2 ]x1 + [2] >= [-2 2 ]x1 + [2] = a(x1) 187.21/47.73 187.21/47.73 [0 4] [4] 187.21/47.73 c(c(x1)) = [0 4]x1 + [4] >= x1 = x1 187.21/47.73 problem: 187.21/47.73 DPs: 187.21/47.73 b#(b(c(x1))) -> a#(x1) 187.21/47.73 a#(x1) -> b#(x1) 187.21/47.73 TRS: 187.21/47.73 a(x1) -> c(b(c(b(b(x1))))) 187.21/47.73 b(b(c(x1))) -> a(x1) 187.21/47.73 c(c(x1)) -> x1 187.21/47.73 Restore Modifier: 187.21/47.73 DPs: 187.21/47.73 b#(b(c(x1))) -> a#(x1) 187.21/47.73 a#(x1) -> b#(x1) 187.21/47.73 TRS: 187.21/47.73 a(x1) -> c(b(c(b(b(x1))))) 187.21/47.73 b(b(c(x1))) -> a(x1) 187.21/47.73 c(c(x1)) -> x1 187.21/47.73 EDG Processor: 187.21/47.73 DPs: 187.21/47.73 b#(b(c(x1))) -> a#(x1) 187.21/47.73 a#(x1) -> b#(x1) 187.21/47.73 TRS: 187.21/47.73 a(x1) -> c(b(c(b(b(x1))))) 187.21/47.73 b(b(c(x1))) -> a(x1) 187.21/47.73 c(c(x1)) -> x1 187.21/47.73 graph: 187.21/47.73 b#(b(c(x1))) -> a#(x1) -> a#(x1) -> b#(x1) 187.21/47.73 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> a#(x1) 187.21/47.73 Usable Rule Processor: 187.21/47.73 DPs: 187.21/47.73 b#(b(c(x1))) -> a#(x1) 187.21/47.73 a#(x1) -> b#(x1) 187.21/47.73 TRS: 187.21/47.73 187.21/47.73 Arctic Interpretation Processor: 187.21/47.73 dimension: 1 187.21/47.73 usable rules: 187.21/47.73 187.21/47.73 interpretation: 187.21/47.73 [b#](x0) = x0, 187.21/47.73 187.21/47.73 [a#](x0) = x0, 187.21/47.73 187.21/47.73 [b](x0) = x0, 187.21/47.73 187.21/47.73 [c](x0) = 1x0 187.21/47.73 orientation: 187.21/47.73 b#(b(c(x1))) = 1x1 >= x1 = a#(x1) 187.21/47.73 187.21/47.73 a#(x1) = x1 >= x1 = b#(x1) 187.21/47.73 problem: 187.21/47.73 DPs: 187.21/47.73 a#(x1) -> b#(x1) 187.21/47.73 TRS: 187.21/47.73 187.21/47.73 Restore Modifier: 187.21/47.73 DPs: 187.21/47.73 a#(x1) -> b#(x1) 187.21/47.73 TRS: 187.21/47.73 a(x1) -> c(b(c(b(b(x1))))) 187.21/47.73 b(b(c(x1))) -> a(x1) 187.21/47.73 c(c(x1)) -> x1 187.21/47.73 EDG Processor: 187.21/47.73 DPs: 187.21/47.73 a#(x1) -> b#(x1) 187.21/47.73 TRS: 187.21/47.73 a(x1) -> c(b(c(b(b(x1))))) 187.21/47.73 b(b(c(x1))) -> a(x1) 187.21/47.73 c(c(x1)) -> x1 187.21/47.73 graph: 187.21/47.73 187.21/47.73 SCC Processor: 187.21/47.73 #sccs: 0 187.21/47.73 #rules: 0 187.21/47.73 #arcs: 0/1 187.21/47.73 187.21/47.73 EOF