176.14/44.97 YES 176.14/44.98 176.14/44.98 Problem: 176.14/44.98 a(x1) -> x1 176.14/44.98 a(a(b(a(x1)))) -> b(b(a(a(a(x1))))) 176.14/44.98 b(x1) -> a(x1) 176.14/44.98 176.14/44.98 Proof: 176.14/44.98 DP Processor: 176.14/44.98 DPs: 176.14/44.98 a#(a(b(a(x1)))) -> a#(a(x1)) 176.14/44.98 a#(a(b(a(x1)))) -> a#(a(a(x1))) 176.14/44.98 a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) 176.14/44.98 a#(a(b(a(x1)))) -> b#(b(a(a(a(x1))))) 176.14/44.98 b#(x1) -> a#(x1) 176.14/44.98 TRS: 176.14/44.98 a(x1) -> x1 176.14/44.98 a(a(b(a(x1)))) -> b(b(a(a(a(x1))))) 176.14/44.98 b(x1) -> a(x1) 176.14/44.98 TDG Processor: 176.14/44.98 DPs: 176.14/44.98 a#(a(b(a(x1)))) -> a#(a(x1)) 176.14/44.98 a#(a(b(a(x1)))) -> a#(a(a(x1))) 176.14/44.98 a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) 176.14/44.98 a#(a(b(a(x1)))) -> b#(b(a(a(a(x1))))) 176.14/44.98 b#(x1) -> a#(x1) 176.14/44.98 TRS: 176.14/44.98 a(x1) -> x1 176.14/44.98 a(a(b(a(x1)))) -> b(b(a(a(a(x1))))) 176.14/44.98 b(x1) -> a(x1) 176.14/44.98 graph: 176.14/44.98 b#(x1) -> a#(x1) -> a#(a(b(a(x1)))) -> b#(b(a(a(a(x1))))) 176.14/44.98 b#(x1) -> a#(x1) -> a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) 176.14/44.98 b#(x1) -> a#(x1) -> a#(a(b(a(x1)))) -> a#(a(a(x1))) 176.14/44.98 b#(x1) -> a#(x1) -> a#(a(b(a(x1)))) -> a#(a(x1)) 176.14/44.98 a#(a(b(a(x1)))) -> b#(b(a(a(a(x1))))) -> b#(x1) -> a#(x1) 176.14/44.98 a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) -> b#(x1) -> a#(x1) 176.14/44.98 a#(a(b(a(x1)))) -> a#(a(a(x1))) -> 176.14/44.98 a#(a(b(a(x1)))) -> b#(b(a(a(a(x1))))) 176.14/44.98 a#(a(b(a(x1)))) -> a#(a(a(x1))) -> 176.14/44.98 a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) 176.14/44.98 a#(a(b(a(x1)))) -> a#(a(a(x1))) -> 176.14/44.98 a#(a(b(a(x1)))) -> a#(a(a(x1))) 176.14/44.98 a#(a(b(a(x1)))) -> a#(a(a(x1))) -> a#(a(b(a(x1)))) -> a#(a(x1)) 176.14/44.98 a#(a(b(a(x1)))) -> a#(a(x1)) -> 176.14/44.98 a#(a(b(a(x1)))) -> b#(b(a(a(a(x1))))) 176.14/44.98 a#(a(b(a(x1)))) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) 176.14/44.98 a#(a(b(a(x1)))) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> a#(a(a(x1))) 176.14/44.98 a#(a(b(a(x1)))) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> a#(a(x1)) 176.14/44.98 Arctic Interpretation Processor: 176.14/44.98 dimension: 2 176.14/44.98 usable rules: 176.14/44.98 a(x1) -> x1 176.14/44.98 a(a(b(a(x1)))) -> b(b(a(a(a(x1))))) 176.14/44.98 b(x1) -> a(x1) 176.14/44.98 interpretation: 176.14/44.98 [b#](x0) = [0 0]x0 + [1], 176.14/44.98 176.14/44.98 [a#](x0) = [0 0]x0 + [0], 176.14/44.98 176.14/44.98 [0 0] [0] 176.14/44.98 [b](x0) = [1 0]x0 + [1], 176.14/44.98 176.14/44.98 [0 0] 176.14/44.98 [a](x0) = [0 0]x0 176.14/44.98 orientation: 176.14/44.98 a#(a(b(a(x1)))) = [1 1]x1 + [1] >= [0 0]x1 + [0] = a#(a(x1)) 176.14/44.98 176.14/44.98 a#(a(b(a(x1)))) = [1 1]x1 + [1] >= [0 0]x1 + [0] = a#(a(a(x1))) 176.14/44.98 176.14/44.98 a#(a(b(a(x1)))) = [1 1]x1 + [1] >= [0 0]x1 + [1] = b#(a(a(a(x1)))) 176.14/44.98 176.14/44.98 a#(a(b(a(x1)))) = [1 1]x1 + [1] >= [1 1]x1 + [1] = b#(b(a(a(a(x1))))) 176.14/44.98 176.14/44.98 b#(x1) = [0 0]x1 + [1] >= [0 0]x1 + [0] = a#(x1) 176.14/44.98 176.14/44.98 [0 0] 176.14/44.98 a(x1) = [0 0]x1 >= x1 = x1 176.14/44.98 176.14/44.98 [1 1] [1] [1 1] [1] 176.14/44.98 a(a(b(a(x1)))) = [1 1]x1 + [1] >= [1 1]x1 + [1] = b(b(a(a(a(x1))))) 176.14/44.98 176.14/44.98 [0 0] [0] [0 0] 176.14/44.98 b(x1) = [1 0]x1 + [1] >= [0 0]x1 = a(x1) 176.14/44.98 problem: 176.14/44.98 DPs: 176.14/44.98 a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) 176.14/44.98 a#(a(b(a(x1)))) -> b#(b(a(a(a(x1))))) 176.14/44.98 b#(x1) -> a#(x1) 176.14/44.98 TRS: 176.14/44.98 a(x1) -> x1 176.14/44.98 a(a(b(a(x1)))) -> b(b(a(a(a(x1))))) 176.14/44.98 b(x1) -> a(x1) 176.14/44.98 Restore Modifier: 176.14/44.98 DPs: 176.14/44.98 a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) 176.14/44.98 a#(a(b(a(x1)))) -> b#(b(a(a(a(x1))))) 176.14/44.98 b#(x1) -> a#(x1) 176.14/44.98 TRS: 176.14/44.98 a(x1) -> x1 176.14/44.98 a(a(b(a(x1)))) -> b(b(a(a(a(x1))))) 176.14/44.98 b(x1) -> a(x1) 176.14/44.99 EDG Processor: 176.14/44.99 DPs: 176.14/44.99 a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) 176.14/44.99 a#(a(b(a(x1)))) -> b#(b(a(a(a(x1))))) 176.14/44.99 b#(x1) -> a#(x1) 176.14/44.99 TRS: 176.14/44.99 a(x1) -> x1 176.14/44.99 a(a(b(a(x1)))) -> b(b(a(a(a(x1))))) 176.14/44.99 b(x1) -> a(x1) 176.14/44.99 graph: 176.14/44.99 b#(x1) -> a#(x1) -> a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) 176.14/44.99 b#(x1) -> a#(x1) -> 176.14/44.99 a#(a(b(a(x1)))) -> b#(b(a(a(a(x1))))) 176.14/44.99 a#(a(b(a(x1)))) -> b#(b(a(a(a(x1))))) -> b#(x1) -> a#(x1) 176.14/44.99 a#(a(b(a(x1)))) -> b#(a(a(a(x1)))) -> b#(x1) -> a#(x1) 176.14/44.99 Arctic Interpretation Processor: 176.14/44.99 dimension: 2 176.14/44.99 usable rules: 176.14/44.99 a(x1) -> x1 176.14/44.99 a(a(b(a(x1)))) -> b(b(a(a(a(x1))))) 176.14/44.99 b(x1) -> a(x1) 176.14/44.99 interpretation: 176.14/44.99 [b#](x0) = [1 3]x0, 176.14/44.99 176.14/44.99 [a#](x0) = [0 0]x0, 176.14/44.99 176.14/44.99 [0 3] [0] 176.14/44.99 [b](x0) = [0 0]x0 + [0], 176.14/44.99 176.14/44.99 [0 3 ] 176.14/44.99 [a](x0) = [-& 0 ]x0 176.14/44.99 orientation: 176.14/44.99 a#(a(b(a(x1)))) = [3 6]x1 + [3] >= [1 4]x1 = b#(a(a(a(x1)))) 176.14/44.99 176.14/44.99 a#(a(b(a(x1)))) = [3 6]x1 + [3] >= [3 6]x1 + [3] = b#(b(a(a(a(x1))))) 176.14/44.99 176.14/44.99 b#(x1) = [1 3]x1 >= [0 0]x1 = a#(x1) 176.14/44.99 176.14/44.99 [0 3 ] 176.14/44.99 a(x1) = [-& 0 ]x1 >= x1 = x1 176.14/44.99 176.14/44.99 [3 6] [3] [3 6] [3] 176.14/44.99 a(a(b(a(x1)))) = [0 3]x1 + [0] >= [0 3]x1 + [0] = b(b(a(a(a(x1))))) 176.14/44.99 176.14/44.99 [0 3] [0] [0 3 ] 176.14/44.99 b(x1) = [0 0]x1 + [0] >= [-& 0 ]x1 = a(x1) 176.14/44.99 problem: 176.14/44.99 DPs: 176.14/44.99 a#(a(b(a(x1)))) -> b#(b(a(a(a(x1))))) 176.14/44.99 TRS: 176.14/44.99 a(x1) -> x1 176.14/44.99 a(a(b(a(x1)))) -> b(b(a(a(a(x1))))) 176.14/44.99 b(x1) -> a(x1) 176.14/44.99 Restore Modifier: 176.14/44.99 DPs: 176.14/44.99 a#(a(b(a(x1)))) -> b#(b(a(a(a(x1))))) 176.14/44.99 TRS: 176.14/44.99 a(x1) -> x1 176.14/44.99 a(a(b(a(x1)))) -> b(b(a(a(a(x1))))) 176.14/44.99 b(x1) -> a(x1) 176.14/44.99 EDG Processor: 176.14/44.99 DPs: 176.14/44.99 a#(a(b(a(x1)))) -> b#(b(a(a(a(x1))))) 176.14/44.99 TRS: 176.14/44.99 a(x1) -> x1 176.14/44.99 a(a(b(a(x1)))) -> b(b(a(a(a(x1))))) 176.14/44.99 b(x1) -> a(x1) 176.14/44.99 graph: 176.14/44.99 176.14/44.99 SCC Processor: 176.14/44.99 #sccs: 0 176.14/44.99 #rules: 0 176.14/44.99 #arcs: 0/1 176.14/44.99 176.14/44.99 EOF