172.69/44.19 YES 172.69/44.20 172.69/44.20 Problem: 172.69/44.20 a(a(b(a(x1)))) -> a(b(b(x1))) 172.69/44.20 b(b(x1)) -> b(a(a(a(x1)))) 172.69/44.20 172.69/44.20 Proof: 172.69/44.20 DP Processor: 172.69/44.20 DPs: 172.69/44.20 a#(a(b(a(x1)))) -> b#(x1) 172.69/44.20 a#(a(b(a(x1)))) -> b#(b(x1)) 172.69/44.20 a#(a(b(a(x1)))) -> a#(b(b(x1))) 172.69/44.20 b#(b(x1)) -> a#(x1) 172.69/44.20 b#(b(x1)) -> a#(a(x1)) 172.69/44.20 b#(b(x1)) -> a#(a(a(x1))) 172.69/44.20 b#(b(x1)) -> b#(a(a(a(x1)))) 172.69/44.20 TRS: 172.69/44.20 a(a(b(a(x1)))) -> a(b(b(x1))) 172.69/44.20 b(b(x1)) -> b(a(a(a(x1)))) 172.69/44.20 TDG Processor: 172.69/44.20 DPs: 172.69/44.20 a#(a(b(a(x1)))) -> b#(x1) 172.69/44.20 a#(a(b(a(x1)))) -> b#(b(x1)) 172.69/44.20 a#(a(b(a(x1)))) -> a#(b(b(x1))) 172.69/44.20 b#(b(x1)) -> a#(x1) 172.69/44.20 b#(b(x1)) -> a#(a(x1)) 172.69/44.20 b#(b(x1)) -> a#(a(a(x1))) 172.69/44.20 b#(b(x1)) -> b#(a(a(a(x1)))) 172.69/44.20 TRS: 172.69/44.20 a(a(b(a(x1)))) -> a(b(b(x1))) 172.69/44.20 b(b(x1)) -> b(a(a(a(x1)))) 172.69/44.20 graph: 172.69/44.20 b#(b(x1)) -> b#(a(a(a(x1)))) -> b#(b(x1)) -> b#(a(a(a(x1)))) 172.69/44.20 b#(b(x1)) -> b#(a(a(a(x1)))) -> b#(b(x1)) -> a#(a(a(x1))) 172.69/44.20 b#(b(x1)) -> b#(a(a(a(x1)))) -> b#(b(x1)) -> a#(a(x1)) 172.69/44.20 b#(b(x1)) -> b#(a(a(a(x1)))) -> b#(b(x1)) -> a#(x1) 172.69/44.20 b#(b(x1)) -> a#(a(a(x1))) -> a#(a(b(a(x1)))) -> a#(b(b(x1))) 172.69/44.20 b#(b(x1)) -> a#(a(a(x1))) -> a#(a(b(a(x1)))) -> b#(b(x1)) 172.69/44.20 b#(b(x1)) -> a#(a(a(x1))) -> a#(a(b(a(x1)))) -> b#(x1) 172.69/44.20 b#(b(x1)) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> a#(b(b(x1))) 172.69/44.20 b#(b(x1)) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> b#(b(x1)) 172.69/44.20 b#(b(x1)) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> b#(x1) 172.69/44.20 b#(b(x1)) -> a#(x1) -> a#(a(b(a(x1)))) -> a#(b(b(x1))) 172.69/44.20 b#(b(x1)) -> a#(x1) -> a#(a(b(a(x1)))) -> b#(b(x1)) 172.69/44.20 b#(b(x1)) -> a#(x1) -> a#(a(b(a(x1)))) -> b#(x1) 172.69/44.20 a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(b(x1)) -> b#(a(a(a(x1)))) 172.69/44.20 a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(b(x1)) -> a#(a(a(x1))) 172.69/44.20 a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(b(x1)) -> a#(a(x1)) 172.69/44.20 a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(b(x1)) -> a#(x1) 172.69/44.20 a#(a(b(a(x1)))) -> b#(x1) -> b#(b(x1)) -> b#(a(a(a(x1)))) 172.69/44.20 a#(a(b(a(x1)))) -> b#(x1) -> b#(b(x1)) -> a#(a(a(x1))) 172.69/44.20 a#(a(b(a(x1)))) -> b#(x1) -> b#(b(x1)) -> a#(a(x1)) 172.69/44.20 a#(a(b(a(x1)))) -> b#(x1) -> b#(b(x1)) -> a#(x1) 172.69/44.20 a#(a(b(a(x1)))) -> a#(b(b(x1))) -> 172.69/44.20 a#(a(b(a(x1)))) -> a#(b(b(x1))) 172.69/44.20 a#(a(b(a(x1)))) -> a#(b(b(x1))) -> a#(a(b(a(x1)))) -> b#(b(x1)) 172.69/44.20 a#(a(b(a(x1)))) -> a#(b(b(x1))) -> a#(a(b(a(x1)))) -> b#(x1) 172.69/44.20 EDG Processor: 172.69/44.20 DPs: 172.69/44.20 a#(a(b(a(x1)))) -> b#(x1) 172.69/44.20 a#(a(b(a(x1)))) -> b#(b(x1)) 172.69/44.20 a#(a(b(a(x1)))) -> a#(b(b(x1))) 172.69/44.20 b#(b(x1)) -> a#(x1) 172.69/44.20 b#(b(x1)) -> a#(a(x1)) 172.69/44.20 b#(b(x1)) -> a#(a(a(x1))) 172.69/44.20 b#(b(x1)) -> b#(a(a(a(x1)))) 172.69/44.20 TRS: 172.69/44.20 a(a(b(a(x1)))) -> a(b(b(x1))) 172.69/44.20 b(b(x1)) -> b(a(a(a(x1)))) 172.69/44.20 graph: 172.69/44.20 b#(b(x1)) -> a#(a(a(x1))) -> a#(a(b(a(x1)))) -> b#(x1) 172.69/44.20 b#(b(x1)) -> a#(a(a(x1))) -> a#(a(b(a(x1)))) -> b#(b(x1)) 172.69/44.20 b#(b(x1)) -> a#(a(a(x1))) -> a#(a(b(a(x1)))) -> a#(b(b(x1))) 172.69/44.20 b#(b(x1)) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> b#(x1) 172.69/44.20 b#(b(x1)) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> b#(b(x1)) 172.69/44.20 b#(b(x1)) -> a#(a(x1)) -> a#(a(b(a(x1)))) -> a#(b(b(x1))) 172.69/44.20 b#(b(x1)) -> a#(x1) -> a#(a(b(a(x1)))) -> b#(x1) 172.69/44.20 b#(b(x1)) -> a#(x1) -> a#(a(b(a(x1)))) -> b#(b(x1)) 172.69/44.20 b#(b(x1)) -> a#(x1) -> a#(a(b(a(x1)))) -> a#(b(b(x1))) 172.69/44.20 a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(b(x1)) -> a#(x1) 172.69/44.20 a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(b(x1)) -> a#(a(x1)) 172.69/44.20 a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(b(x1)) -> a#(a(a(x1))) 172.69/44.20 a#(a(b(a(x1)))) -> b#(b(x1)) -> b#(b(x1)) -> b#(a(a(a(x1)))) 172.69/44.20 a#(a(b(a(x1)))) -> b#(x1) -> b#(b(x1)) -> a#(x1) 172.69/44.20 a#(a(b(a(x1)))) -> b#(x1) -> b#(b(x1)) -> a#(a(x1)) 172.69/44.20 a#(a(b(a(x1)))) -> b#(x1) -> b#(b(x1)) -> a#(a(a(x1))) 172.69/44.20 a#(a(b(a(x1)))) -> b#(x1) -> b#(b(x1)) -> b#(a(a(a(x1)))) 172.69/44.20 SCC Processor: 172.69/44.20 #sccs: 1 172.69/44.20 #rules: 5 172.69/44.20 #arcs: 17/49 172.69/44.20 DPs: 172.69/44.20 b#(b(x1)) -> a#(a(a(x1))) 172.69/44.20 a#(a(b(a(x1)))) -> b#(b(x1)) 172.69/44.20 b#(b(x1)) -> a#(a(x1)) 172.69/44.20 a#(a(b(a(x1)))) -> b#(x1) 172.69/44.20 b#(b(x1)) -> a#(x1) 172.69/44.20 TRS: 172.69/44.20 a(a(b(a(x1)))) -> a(b(b(x1))) 172.69/44.20 b(b(x1)) -> b(a(a(a(x1)))) 172.69/44.20 Arctic Interpretation Processor: 172.69/44.20 dimension: 2 172.69/44.20 usable rules: 172.69/44.20 a(a(b(a(x1)))) -> a(b(b(x1))) 172.69/44.20 b(b(x1)) -> b(a(a(a(x1)))) 172.69/44.20 interpretation: 172.69/44.20 [b#](x0) = [-& 1 ]x0 + [0], 172.69/44.20 172.69/44.20 [a#](x0) = [-& 1 ]x0 + [0], 172.69/44.20 172.69/44.20 [0 2] [0 ] 172.69/44.20 [b](x0) = [0 0]x0 + [-&], 172.69/44.20 172.69/44.20 [0 0] 172.69/44.20 [a](x0) = [0 0]x0 172.69/44.20 orientation: 172.69/44.20 b#(b(x1)) = [1 1]x1 + [0] >= [1 1]x1 + [0] = a#(a(a(x1))) 172.69/44.20 172.69/44.20 a#(a(b(a(x1)))) = [3 3]x1 + [1] >= [1 1]x1 + [0] = b#(b(x1)) 172.69/44.20 172.69/44.20 b#(b(x1)) = [1 1]x1 + [0] >= [1 1]x1 + [0] = a#(a(x1)) 172.69/44.20 172.69/44.20 a#(a(b(a(x1)))) = [3 3]x1 + [1] >= [-& 1 ]x1 + [0] = b#(x1) 172.69/44.20 172.69/44.20 b#(b(x1)) = [1 1]x1 + [0] >= [-& 1 ]x1 + [0] = a#(x1) 172.69/44.20 172.69/44.20 [2 2] [0] [2 2] [0] 172.69/44.20 a(a(b(a(x1)))) = [2 2]x1 + [0] >= [2 2]x1 + [0] = a(b(b(x1))) 172.69/44.20 172.69/44.20 [2 2] [0] [2 2] [0 ] 172.69/44.20 b(b(x1)) = [0 2]x1 + [0] >= [0 0]x1 + [-&] = b(a(a(a(x1)))) 172.69/44.20 problem: 172.69/44.20 DPs: 172.69/44.20 b#(b(x1)) -> a#(a(a(x1))) 172.69/44.20 b#(b(x1)) -> a#(a(x1)) 172.69/44.20 b#(b(x1)) -> a#(x1) 172.69/44.20 TRS: 172.69/44.20 a(a(b(a(x1)))) -> a(b(b(x1))) 172.69/44.20 b(b(x1)) -> b(a(a(a(x1)))) 172.69/44.20 Restore Modifier: 172.69/44.20 DPs: 172.69/44.20 b#(b(x1)) -> a#(a(a(x1))) 172.69/44.20 b#(b(x1)) -> a#(a(x1)) 172.69/44.20 b#(b(x1)) -> a#(x1) 172.69/44.20 TRS: 172.69/44.20 a(a(b(a(x1)))) -> a(b(b(x1))) 172.69/44.20 b(b(x1)) -> b(a(a(a(x1)))) 172.69/44.20 EDG Processor: 172.69/44.20 DPs: 172.69/44.20 b#(b(x1)) -> a#(a(a(x1))) 172.69/44.20 b#(b(x1)) -> a#(a(x1)) 172.69/44.20 b#(b(x1)) -> a#(x1) 172.69/44.20 TRS: 172.69/44.20 a(a(b(a(x1)))) -> a(b(b(x1))) 172.69/44.20 b(b(x1)) -> b(a(a(a(x1)))) 172.69/44.20 graph: 172.69/44.20 172.69/44.20 SCC Processor: 172.69/44.20 #sccs: 0 172.69/44.20 #rules: 0 172.69/44.20 #arcs: 0/9 172.69/44.20 172.69/44.21 EOF