183.67/46.94 YES 183.67/46.95 183.67/46.95 Problem: 183.67/46.95 a(x1) -> x1 183.67/46.95 a(b(x1)) -> c(a(x1)) 183.67/46.95 c(c(x1)) -> c(b(c(b(a(x1))))) 183.67/46.95 183.67/46.95 Proof: 183.67/46.95 String Reversal Processor: 183.67/46.95 a(x1) -> x1 183.67/46.95 b(a(x1)) -> a(c(x1)) 183.67/46.95 c(c(x1)) -> a(b(c(b(c(x1))))) 183.67/46.95 DP Processor: 183.67/46.95 DPs: 183.67/46.95 b#(a(x1)) -> c#(x1) 183.67/46.95 b#(a(x1)) -> a#(c(x1)) 183.67/46.95 c#(c(x1)) -> b#(c(x1)) 183.67/46.95 c#(c(x1)) -> c#(b(c(x1))) 183.67/46.95 c#(c(x1)) -> b#(c(b(c(x1)))) 183.67/46.95 c#(c(x1)) -> a#(b(c(b(c(x1))))) 183.67/46.95 TRS: 183.67/46.95 a(x1) -> x1 183.67/46.95 b(a(x1)) -> a(c(x1)) 183.67/46.95 c(c(x1)) -> a(b(c(b(c(x1))))) 183.67/46.95 TDG Processor: 183.67/46.95 DPs: 183.67/46.95 b#(a(x1)) -> c#(x1) 183.67/46.95 b#(a(x1)) -> a#(c(x1)) 183.67/46.95 c#(c(x1)) -> b#(c(x1)) 183.67/46.95 c#(c(x1)) -> c#(b(c(x1))) 183.67/46.95 c#(c(x1)) -> b#(c(b(c(x1)))) 183.67/46.95 c#(c(x1)) -> a#(b(c(b(c(x1))))) 183.67/46.95 TRS: 183.67/46.95 a(x1) -> x1 183.67/46.95 b(a(x1)) -> a(c(x1)) 183.67/46.95 c(c(x1)) -> a(b(c(b(c(x1))))) 183.67/46.95 graph: 183.67/46.95 c#(c(x1)) -> c#(b(c(x1))) -> c#(c(x1)) -> a#(b(c(b(c(x1))))) 183.67/46.95 c#(c(x1)) -> c#(b(c(x1))) -> c#(c(x1)) -> b#(c(b(c(x1)))) 183.67/46.95 c#(c(x1)) -> c#(b(c(x1))) -> c#(c(x1)) -> c#(b(c(x1))) 183.67/46.95 c#(c(x1)) -> c#(b(c(x1))) -> c#(c(x1)) -> b#(c(x1)) 183.67/46.95 c#(c(x1)) -> b#(c(b(c(x1)))) -> b#(a(x1)) -> a#(c(x1)) 183.67/46.95 c#(c(x1)) -> b#(c(b(c(x1)))) -> b#(a(x1)) -> c#(x1) 183.67/46.95 c#(c(x1)) -> b#(c(x1)) -> b#(a(x1)) -> a#(c(x1)) 183.67/46.95 c#(c(x1)) -> b#(c(x1)) -> b#(a(x1)) -> c#(x1) 183.67/46.95 b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> a#(b(c(b(c(x1))))) 183.67/46.95 b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> b#(c(b(c(x1)))) 183.67/46.95 b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> c#(b(c(x1))) 183.67/46.95 b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> b#(c(x1)) 183.67/46.95 SCC Processor: 183.67/46.95 #sccs: 1 183.67/46.95 #rules: 4 183.67/46.95 #arcs: 12/36 183.67/46.95 DPs: 183.67/46.95 c#(c(x1)) -> c#(b(c(x1))) 183.67/46.95 c#(c(x1)) -> b#(c(x1)) 183.67/46.95 b#(a(x1)) -> c#(x1) 183.67/46.95 c#(c(x1)) -> b#(c(b(c(x1)))) 183.67/46.95 TRS: 183.67/46.95 a(x1) -> x1 183.67/46.95 b(a(x1)) -> a(c(x1)) 183.67/46.95 c(c(x1)) -> a(b(c(b(c(x1))))) 183.67/46.95 Arctic Interpretation Processor: 183.67/46.95 dimension: 2 183.67/46.95 usable rules: 183.67/46.95 a(x1) -> x1 183.67/46.95 b(a(x1)) -> a(c(x1)) 183.67/46.95 c(c(x1)) -> a(b(c(b(c(x1))))) 183.67/46.95 interpretation: 183.67/46.95 [c#](x0) = [1 0]x0 + [0], 183.67/46.95 183.67/46.95 [b#](x0) = [1 0]x0 + [0], 183.67/46.95 183.67/46.95 [1 0 ] [1] 183.67/46.95 [c](x0) = [0 -&]x0 + [0], 183.67/46.95 183.67/46.95 [-& 0 ] [0] 183.67/46.95 [b](x0) = [0 1 ]x0 + [0], 183.67/46.95 183.67/46.95 [0 1] [0] 183.67/46.95 [a](x0) = [1 0]x0 + [1] 183.67/46.95 orientation: 183.67/46.95 c#(c(x1)) = [2 1]x1 + [2] >= [1 0]x1 + [1] = c#(b(c(x1))) 183.67/46.95 183.67/46.95 c#(c(x1)) = [2 1]x1 + [2] >= [2 1]x1 + [2] = b#(c(x1)) 183.67/46.95 183.67/46.95 b#(a(x1)) = [1 2]x1 + [1] >= [1 0]x1 + [0] = c#(x1) 183.67/46.95 183.67/46.95 c#(c(x1)) = [2 1]x1 + [2] >= [2 1]x1 + [2] = b#(c(b(c(x1)))) 183.67/46.95 183.67/46.95 [0 1] [0] 183.67/46.95 a(x1) = [1 0]x1 + [1] >= x1 = x1 183.67/46.95 183.67/46.95 [1 0] [1] [1 0] [1] 183.67/46.95 b(a(x1)) = [2 1]x1 + [2] >= [2 1]x1 + [2] = a(c(x1)) 183.67/46.95 183.67/46.95 [2 1] [2] [2 1] [2] 183.67/46.95 c(c(x1)) = [1 0]x1 + [1] >= [1 0]x1 + [1] = a(b(c(b(c(x1))))) 183.67/46.95 problem: 183.67/46.95 DPs: 183.67/46.95 c#(c(x1)) -> b#(c(x1)) 183.67/46.95 b#(a(x1)) -> c#(x1) 183.67/46.95 c#(c(x1)) -> b#(c(b(c(x1)))) 183.67/46.95 TRS: 183.67/46.95 a(x1) -> x1 183.67/46.95 b(a(x1)) -> a(c(x1)) 183.67/46.95 c(c(x1)) -> a(b(c(b(c(x1))))) 183.67/46.95 Restore Modifier: 183.67/46.95 DPs: 183.67/46.95 c#(c(x1)) -> b#(c(x1)) 183.67/46.95 b#(a(x1)) -> c#(x1) 183.67/46.95 c#(c(x1)) -> b#(c(b(c(x1)))) 183.67/46.95 TRS: 183.67/46.95 a(x1) -> x1 183.67/46.95 b(a(x1)) -> a(c(x1)) 183.67/46.95 c(c(x1)) -> a(b(c(b(c(x1))))) 183.67/46.95 EDG Processor: 183.67/46.95 DPs: 183.67/46.95 c#(c(x1)) -> b#(c(x1)) 183.67/46.95 b#(a(x1)) -> c#(x1) 183.67/46.95 c#(c(x1)) -> b#(c(b(c(x1)))) 183.67/46.95 TRS: 183.67/46.95 a(x1) -> x1 183.67/46.95 b(a(x1)) -> a(c(x1)) 183.67/46.95 c(c(x1)) -> a(b(c(b(c(x1))))) 183.67/46.95 graph: 183.67/46.95 c#(c(x1)) -> b#(c(b(c(x1)))) -> b#(a(x1)) -> c#(x1) 183.67/46.95 c#(c(x1)) -> b#(c(x1)) -> b#(a(x1)) -> c#(x1) 183.67/46.95 b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> b#(c(x1)) 183.67/46.95 b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> b#(c(b(c(x1)))) 183.67/46.95 Arctic Interpretation Processor: 183.67/46.95 dimension: 2 183.67/46.95 usable rules: 183.67/46.95 a(x1) -> x1 183.67/46.95 b(a(x1)) -> a(c(x1)) 183.67/46.95 c(c(x1)) -> a(b(c(b(c(x1))))) 183.67/46.95 interpretation: 183.67/46.95 [c#](x0) = [1 0]x0 + [2], 183.67/46.95 183.67/46.95 [b#](x0) = [0 0]x0 + [0], 183.67/46.95 183.67/46.95 [1 0 ] [2] 183.67/46.95 [c](x0) = [0 -&]x0 + [0], 183.67/46.95 183.67/46.95 [-& 0 ] [1] 183.67/46.95 [b](x0) = [0 1 ]x0 + [0], 183.67/46.95 183.67/46.95 [0 0] [0] 183.67/46.95 [a](x0) = [1 0]x0 + [2] 183.67/46.95 orientation: 183.67/46.95 c#(c(x1)) = [2 1]x1 + [3] >= [1 0]x1 + [2] = b#(c(x1)) 183.67/46.95 183.67/46.95 b#(a(x1)) = [1 0]x1 + [2] >= [1 0]x1 + [2] = c#(x1) 183.67/46.95 183.67/46.95 c#(c(x1)) = [2 1]x1 + [3] >= [1 0]x1 + [2] = b#(c(b(c(x1)))) 183.67/46.95 183.67/46.95 [0 0] [0] 183.67/46.95 a(x1) = [1 0]x1 + [2] >= x1 = x1 183.67/46.95 183.67/46.95 [1 0] [2] [1 0] [2] 183.67/46.95 b(a(x1)) = [2 1]x1 + [3] >= [2 1]x1 + [3] = a(c(x1)) 183.67/46.95 183.67/46.95 [2 1] [3] [1 0] [2] 183.67/46.95 c(c(x1)) = [1 0]x1 + [2] >= [1 0]x1 + [2] = a(b(c(b(c(x1))))) 183.67/46.95 problem: 183.67/46.95 DPs: 183.67/46.95 b#(a(x1)) -> c#(x1) 183.67/46.95 TRS: 183.67/46.95 a(x1) -> x1 183.67/46.95 b(a(x1)) -> a(c(x1)) 183.67/46.95 c(c(x1)) -> a(b(c(b(c(x1))))) 183.67/46.95 Restore Modifier: 183.67/46.95 DPs: 183.67/46.95 b#(a(x1)) -> c#(x1) 183.67/46.95 TRS: 183.67/46.95 a(x1) -> x1 183.67/46.95 b(a(x1)) -> a(c(x1)) 183.67/46.95 c(c(x1)) -> a(b(c(b(c(x1))))) 183.67/46.95 EDG Processor: 183.67/46.95 DPs: 183.67/46.95 b#(a(x1)) -> c#(x1) 183.67/46.95 TRS: 183.67/46.95 a(x1) -> x1 183.67/46.95 b(a(x1)) -> a(c(x1)) 183.67/46.95 c(c(x1)) -> a(b(c(b(c(x1))))) 183.67/46.95 graph: 183.67/46.95 183.67/46.95 SCC Processor: 183.67/46.95 #sccs: 0 183.67/46.95 #rules: 0 183.67/46.95 #arcs: 0/1 183.67/46.95 183.67/46.96 EOF