178.40/45.56 YES 178.40/45.57 178.40/45.57 Problem: 178.40/45.57 a(x1) -> x1 178.40/45.57 a(a(x1)) -> b(b(c(x1))) 178.40/45.57 c(x1) -> x1 178.40/45.57 c(b(x1)) -> b(c(a(x1))) 178.40/45.57 178.40/45.57 Proof: 178.40/45.57 String Reversal Processor: 178.40/45.57 a(x1) -> x1 178.40/45.57 a(a(x1)) -> c(b(b(x1))) 178.40/45.57 c(x1) -> x1 178.40/45.57 b(c(x1)) -> a(c(b(x1))) 178.40/45.57 DP Processor: 178.40/45.57 DPs: 178.40/45.57 a#(a(x1)) -> b#(x1) 178.40/45.57 a#(a(x1)) -> b#(b(x1)) 178.40/45.57 a#(a(x1)) -> c#(b(b(x1))) 178.40/45.57 b#(c(x1)) -> b#(x1) 178.40/45.57 b#(c(x1)) -> c#(b(x1)) 178.40/45.57 b#(c(x1)) -> a#(c(b(x1))) 178.40/45.57 TRS: 178.40/45.57 a(x1) -> x1 178.40/45.57 a(a(x1)) -> c(b(b(x1))) 178.40/45.57 c(x1) -> x1 178.40/45.57 b(c(x1)) -> a(c(b(x1))) 178.40/45.57 TDG Processor: 178.40/45.57 DPs: 178.40/45.57 a#(a(x1)) -> b#(x1) 178.40/45.57 a#(a(x1)) -> b#(b(x1)) 178.40/45.57 a#(a(x1)) -> c#(b(b(x1))) 178.40/45.57 b#(c(x1)) -> b#(x1) 178.40/45.57 b#(c(x1)) -> c#(b(x1)) 178.40/45.57 b#(c(x1)) -> a#(c(b(x1))) 178.40/45.57 TRS: 178.40/45.57 a(x1) -> x1 178.40/45.57 a(a(x1)) -> c(b(b(x1))) 178.40/45.57 c(x1) -> x1 178.40/45.57 b(c(x1)) -> a(c(b(x1))) 178.40/45.57 graph: 178.40/45.57 b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> a#(c(b(x1))) 178.40/45.57 b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> c#(b(x1)) 178.40/45.57 b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1) 178.40/45.57 b#(c(x1)) -> a#(c(b(x1))) -> a#(a(x1)) -> c#(b(b(x1))) 178.40/45.57 b#(c(x1)) -> a#(c(b(x1))) -> a#(a(x1)) -> b#(b(x1)) 178.40/45.57 b#(c(x1)) -> a#(c(b(x1))) -> a#(a(x1)) -> b#(x1) 178.40/45.57 a#(a(x1)) -> b#(b(x1)) -> b#(c(x1)) -> a#(c(b(x1))) 178.40/45.57 a#(a(x1)) -> b#(b(x1)) -> b#(c(x1)) -> c#(b(x1)) 178.40/45.57 a#(a(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(x1) 178.40/45.57 a#(a(x1)) -> b#(x1) -> b#(c(x1)) -> a#(c(b(x1))) 178.40/45.57 a#(a(x1)) -> b#(x1) -> b#(c(x1)) -> c#(b(x1)) 178.40/45.57 a#(a(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1) 178.40/45.57 SCC Processor: 178.40/45.57 #sccs: 1 178.40/45.57 #rules: 4 178.40/45.57 #arcs: 12/36 178.40/45.57 DPs: 178.40/45.57 b#(c(x1)) -> b#(x1) 178.40/45.57 b#(c(x1)) -> a#(c(b(x1))) 178.40/45.57 a#(a(x1)) -> b#(x1) 178.40/45.57 a#(a(x1)) -> b#(b(x1)) 178.40/45.57 TRS: 178.40/45.57 a(x1) -> x1 178.40/45.57 a(a(x1)) -> c(b(b(x1))) 178.40/45.57 c(x1) -> x1 178.40/45.57 b(c(x1)) -> a(c(b(x1))) 178.40/45.57 Arctic Interpretation Processor: 178.40/45.57 dimension: 2 178.40/45.57 usable rules: 178.40/45.57 a(x1) -> x1 178.40/45.57 a(a(x1)) -> c(b(b(x1))) 178.40/45.57 c(x1) -> x1 178.40/45.57 b(c(x1)) -> a(c(b(x1))) 178.40/45.57 interpretation: 178.40/45.57 [b#](x0) = [-& 2 ]x0 + [0], 178.40/45.57 178.40/45.57 [a#](x0) = [-& 2 ]x0 + [0], 178.40/45.57 178.40/45.57 [0 2 ] 178.40/45.57 [b](x0) = [-& 0 ]x0, 178.40/45.57 178.40/45.57 [0 2] [0] 178.40/45.57 [c](x0) = [0 2]x0 + [0], 178.40/45.57 178.40/45.57 [0 2] [0 ] 178.40/45.57 [a](x0) = [0 0]x0 + [-&] 178.40/45.57 orientation: 178.40/45.57 b#(c(x1)) = [2 4]x1 + [2] >= [-& 2 ]x1 + [0] = b#(x1) 178.40/45.57 178.40/45.57 b#(c(x1)) = [2 4]x1 + [2] >= [2 4]x1 + [2] = a#(c(b(x1))) 178.40/45.57 178.40/45.57 a#(a(x1)) = [2 2]x1 + [0] >= [-& 2 ]x1 + [0] = b#(x1) 178.40/45.57 178.40/45.57 a#(a(x1)) = [2 2]x1 + [0] >= [-& 2 ]x1 + [0] = b#(b(x1)) 178.40/45.57 178.40/45.57 [0 2] [0 ] 178.40/45.57 a(x1) = [0 0]x1 + [-&] >= x1 = x1 178.40/45.57 178.40/45.57 [2 2] [0] [0 2] [0] 178.40/45.57 a(a(x1)) = [0 2]x1 + [0] >= [0 2]x1 + [0] = c(b(b(x1))) 178.40/45.57 178.40/45.57 [0 2] [0] 178.40/45.57 c(x1) = [0 2]x1 + [0] >= x1 = x1 178.40/45.57 178.40/45.57 [2 4] [2] [2 4] [2] 178.40/45.57 b(c(x1)) = [0 2]x1 + [0] >= [0 2]x1 + [0] = a(c(b(x1))) 178.40/45.57 problem: 178.40/45.57 DPs: 178.40/45.57 b#(c(x1)) -> a#(c(b(x1))) 178.40/45.57 a#(a(x1)) -> b#(x1) 178.40/45.57 a#(a(x1)) -> b#(b(x1)) 178.40/45.57 TRS: 178.40/45.57 a(x1) -> x1 178.40/45.57 a(a(x1)) -> c(b(b(x1))) 178.40/45.57 c(x1) -> x1 178.40/45.57 b(c(x1)) -> a(c(b(x1))) 178.40/45.57 Restore Modifier: 178.40/45.57 DPs: 178.40/45.57 b#(c(x1)) -> a#(c(b(x1))) 178.40/45.57 a#(a(x1)) -> b#(x1) 178.40/45.57 a#(a(x1)) -> b#(b(x1)) 178.40/45.57 TRS: 178.40/45.57 a(x1) -> x1 178.40/45.57 a(a(x1)) -> c(b(b(x1))) 178.40/45.57 c(x1) -> x1 178.40/45.57 b(c(x1)) -> a(c(b(x1))) 178.40/45.57 EDG Processor: 178.40/45.57 DPs: 178.40/45.57 b#(c(x1)) -> a#(c(b(x1))) 178.40/45.57 a#(a(x1)) -> b#(x1) 178.40/45.57 a#(a(x1)) -> b#(b(x1)) 178.40/45.57 TRS: 178.40/45.57 a(x1) -> x1 178.40/45.57 a(a(x1)) -> c(b(b(x1))) 178.40/45.57 c(x1) -> x1 178.40/45.57 b(c(x1)) -> a(c(b(x1))) 178.40/45.57 graph: 178.40/45.57 b#(c(x1)) -> a#(c(b(x1))) -> a#(a(x1)) -> b#(x1) 178.40/45.57 b#(c(x1)) -> a#(c(b(x1))) -> a#(a(x1)) -> b#(b(x1)) 178.40/45.57 a#(a(x1)) -> b#(b(x1)) -> b#(c(x1)) -> a#(c(b(x1))) 178.40/45.57 a#(a(x1)) -> b#(x1) -> b#(c(x1)) -> a#(c(b(x1))) 178.40/45.57 Arctic Interpretation Processor: 178.40/45.57 dimension: 2 178.40/45.57 usable rules: 178.40/45.57 a(x1) -> x1 178.40/45.57 a(a(x1)) -> c(b(b(x1))) 178.40/45.57 c(x1) -> x1 178.40/45.57 b(c(x1)) -> a(c(b(x1))) 178.40/45.57 interpretation: 178.40/45.57 [b#](x0) = [0 2]x0 + [0], 178.40/45.57 178.40/45.57 [a#](x0) = [3 2]x0 + [0], 178.40/45.57 178.40/45.57 [0 0] [0] 178.40/45.57 [b](x0) = [0 0]x0 + [1], 178.40/45.57 178.40/45.57 [0 0] [0] 178.40/45.57 [c](x0) = [2 2]x0 + [3], 178.40/45.57 178.40/45.57 [0 0] [2] 178.40/45.57 [a](x0) = [2 0]x0 + [3] 178.40/45.57 orientation: 178.40/45.57 b#(c(x1)) = [4 4]x1 + [5] >= [4 4]x1 + [5] = a#(c(b(x1))) 178.40/45.57 178.40/45.57 a#(a(x1)) = [4 3]x1 + [5] >= [0 2]x1 + [0] = b#(x1) 178.40/45.57 178.40/45.57 a#(a(x1)) = [4 3]x1 + [5] >= [2 2]x1 + [3] = b#(b(x1)) 178.40/45.57 178.40/45.57 [0 0] [2] 178.40/45.57 a(x1) = [2 0]x1 + [3] >= x1 = x1 178.40/45.57 178.40/45.57 [2 0] [3] [0 0] [1] 178.40/45.57 a(a(x1)) = [2 2]x1 + [4] >= [2 2]x1 + [3] = c(b(b(x1))) 178.40/45.57 178.40/45.57 [0 0] [0] 178.40/45.57 c(x1) = [2 2]x1 + [3] >= x1 = x1 178.40/45.57 178.40/45.57 [2 2] [3] [2 2] [3] 178.40/45.57 b(c(x1)) = [2 2]x1 + [3] >= [2 2]x1 + [3] = a(c(b(x1))) 178.40/45.57 problem: 178.40/45.57 DPs: 178.40/45.57 b#(c(x1)) -> a#(c(b(x1))) 178.40/45.57 TRS: 178.40/45.57 a(x1) -> x1 178.40/45.57 a(a(x1)) -> c(b(b(x1))) 178.40/45.57 c(x1) -> x1 178.40/45.57 b(c(x1)) -> a(c(b(x1))) 178.40/45.57 Restore Modifier: 178.40/45.57 DPs: 178.40/45.57 b#(c(x1)) -> a#(c(b(x1))) 178.40/45.57 TRS: 178.40/45.57 a(x1) -> x1 178.40/45.57 a(a(x1)) -> c(b(b(x1))) 178.40/45.57 c(x1) -> x1 178.40/45.57 b(c(x1)) -> a(c(b(x1))) 178.40/45.57 EDG Processor: 178.40/45.57 DPs: 178.40/45.57 b#(c(x1)) -> a#(c(b(x1))) 178.40/45.57 TRS: 178.40/45.57 a(x1) -> x1 178.40/45.57 a(a(x1)) -> c(b(b(x1))) 178.40/45.57 c(x1) -> x1 178.40/45.57 b(c(x1)) -> a(c(b(x1))) 178.40/45.57 graph: 178.40/45.57 178.40/45.57 SCC Processor: 178.40/45.57 #sccs: 0 178.40/45.57 #rules: 0 178.40/45.57 #arcs: 0/1 178.40/45.57 178.40/45.57 EOF