172.36/44.05 YES 172.36/44.05 172.36/44.05 Problem: 172.36/44.05 a(x1) -> b(c(b(x1))) 172.36/44.05 b(b(c(x1))) -> c(a(b(x1))) 172.36/44.05 c(c(x1)) -> x1 172.36/44.05 172.36/44.05 Proof: 172.36/44.05 DP Processor: 172.36/44.05 DPs: 172.36/44.05 a#(x1) -> b#(x1) 172.36/44.05 a#(x1) -> c#(b(x1)) 172.36/44.05 a#(x1) -> b#(c(b(x1))) 172.36/44.05 b#(b(c(x1))) -> b#(x1) 172.36/44.05 b#(b(c(x1))) -> a#(b(x1)) 172.36/44.05 b#(b(c(x1))) -> c#(a(b(x1))) 172.36/44.05 TRS: 172.36/44.05 a(x1) -> b(c(b(x1))) 172.36/44.05 b(b(c(x1))) -> c(a(b(x1))) 172.36/44.05 c(c(x1)) -> x1 172.36/44.05 TDG Processor: 172.36/44.05 DPs: 172.36/44.05 a#(x1) -> b#(x1) 172.36/44.05 a#(x1) -> c#(b(x1)) 172.36/44.05 a#(x1) -> b#(c(b(x1))) 172.36/44.05 b#(b(c(x1))) -> b#(x1) 172.36/44.05 b#(b(c(x1))) -> a#(b(x1)) 172.36/44.05 b#(b(c(x1))) -> c#(a(b(x1))) 172.36/44.05 TRS: 172.36/44.05 a(x1) -> b(c(b(x1))) 172.36/44.05 b(b(c(x1))) -> c(a(b(x1))) 172.36/44.05 c(c(x1)) -> x1 172.36/44.05 graph: 172.36/44.05 b#(b(c(x1))) -> b#(x1) -> b#(b(c(x1))) -> c#(a(b(x1))) 172.36/44.05 b#(b(c(x1))) -> b#(x1) -> b#(b(c(x1))) -> a#(b(x1)) 172.36/44.05 b#(b(c(x1))) -> b#(x1) -> b#(b(c(x1))) -> b#(x1) 172.36/44.05 b#(b(c(x1))) -> a#(b(x1)) -> a#(x1) -> b#(c(b(x1))) 172.36/44.05 b#(b(c(x1))) -> a#(b(x1)) -> a#(x1) -> c#(b(x1)) 172.36/44.05 b#(b(c(x1))) -> a#(b(x1)) -> a#(x1) -> b#(x1) 172.36/44.05 a#(x1) -> b#(c(b(x1))) -> b#(b(c(x1))) -> c#(a(b(x1))) 172.36/44.05 a#(x1) -> b#(c(b(x1))) -> b#(b(c(x1))) -> a#(b(x1)) 172.36/44.05 a#(x1) -> b#(c(b(x1))) -> b#(b(c(x1))) -> b#(x1) 172.36/44.05 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> c#(a(b(x1))) 172.36/44.05 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> a#(b(x1)) 172.36/44.05 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> b#(x1) 172.36/44.05 SCC Processor: 172.36/44.05 #sccs: 1 172.36/44.05 #rules: 4 172.36/44.05 #arcs: 12/36 172.36/44.05 DPs: 172.36/44.05 b#(b(c(x1))) -> b#(x1) 172.36/44.05 b#(b(c(x1))) -> a#(b(x1)) 172.36/44.05 a#(x1) -> b#(x1) 172.36/44.05 a#(x1) -> b#(c(b(x1))) 172.36/44.05 TRS: 172.36/44.05 a(x1) -> b(c(b(x1))) 172.36/44.05 b(b(c(x1))) -> c(a(b(x1))) 172.36/44.05 c(c(x1)) -> x1 172.36/44.05 Arctic Interpretation Processor: 172.36/44.05 dimension: 2 172.36/44.05 usable rules: 172.36/44.05 a(x1) -> b(c(b(x1))) 172.36/44.05 b(b(c(x1))) -> c(a(b(x1))) 172.36/44.05 c(c(x1)) -> x1 172.36/44.05 interpretation: 172.36/44.05 [b#](x0) = [-& 0 ]x0 + [0], 172.36/44.05 172.36/44.05 [a#](x0) = [-& 0 ]x0 + [0], 172.36/44.05 172.36/44.05 [1 0 ] [1 ] 172.36/44.05 [c](x0) = [0 -&]x0 + [-&], 172.36/44.05 172.36/44.05 [-& 0 ] [0 ] 172.36/44.05 [b](x0) = [0 -&]x0 + [-&], 172.36/44.05 172.36/44.05 [-& 0 ] [0] 172.36/44.05 [a](x0) = [0 1 ]x0 + [1] 172.36/44.05 orientation: 172.36/44.05 b#(b(c(x1))) = [1 0]x1 + [1] >= [-& 0 ]x1 + [0] = b#(x1) 172.36/44.05 172.36/44.05 b#(b(c(x1))) = [1 0]x1 + [1] >= [0 -&]x1 + [0] = a#(b(x1)) 172.36/44.05 172.36/44.05 a#(x1) = [-& 0 ]x1 + [0] >= [-& 0 ]x1 + [0] = b#(x1) 172.36/44.05 172.36/44.05 a#(x1) = [-& 0 ]x1 + [0] >= [-& 0 ]x1 + [0] = b#(c(b(x1))) 172.36/44.05 172.36/44.05 [-& 0 ] [0] [-& 0 ] [0] 172.36/44.05 a(x1) = [0 1 ]x1 + [1] >= [0 1 ]x1 + [1] = b(c(b(x1))) 172.36/44.05 172.36/44.05 [1 0 ] [1] [1 0 ] [1] 172.36/44.05 b(b(c(x1))) = [0 -&]x1 + [0] >= [0 -&]x1 + [0] = c(a(b(x1))) 172.36/44.05 172.36/44.05 [2 1] [2] 172.36/44.05 c(c(x1)) = [1 0]x1 + [1] >= x1 = x1 172.36/44.05 problem: 172.36/44.05 DPs: 172.36/44.05 b#(b(c(x1))) -> b#(x1) 172.36/44.05 a#(x1) -> b#(x1) 172.36/44.05 a#(x1) -> b#(c(b(x1))) 172.36/44.05 TRS: 172.36/44.05 a(x1) -> b(c(b(x1))) 172.36/44.05 b(b(c(x1))) -> c(a(b(x1))) 172.36/44.05 c(c(x1)) -> x1 172.36/44.05 Restore Modifier: 172.36/44.05 DPs: 172.36/44.05 b#(b(c(x1))) -> b#(x1) 172.36/44.05 a#(x1) -> b#(x1) 172.36/44.05 a#(x1) -> b#(c(b(x1))) 172.36/44.05 TRS: 172.36/44.05 a(x1) -> b(c(b(x1))) 172.36/44.05 b(b(c(x1))) -> c(a(b(x1))) 172.36/44.05 c(c(x1)) -> x1 172.36/44.05 EDG Processor: 172.36/44.05 DPs: 172.36/44.05 b#(b(c(x1))) -> b#(x1) 172.36/44.05 a#(x1) -> b#(x1) 172.36/44.05 a#(x1) -> b#(c(b(x1))) 172.36/44.05 TRS: 172.36/44.05 a(x1) -> b(c(b(x1))) 172.36/44.05 b(b(c(x1))) -> c(a(b(x1))) 172.36/44.05 c(c(x1)) -> x1 172.36/44.05 graph: 172.36/44.05 b#(b(c(x1))) -> b#(x1) -> b#(b(c(x1))) -> b#(x1) 172.36/44.05 a#(x1) -> b#(c(b(x1))) -> b#(b(c(x1))) -> b#(x1) 172.36/44.05 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> b#(x1) 172.36/44.05 SCC Processor: 172.36/44.05 #sccs: 1 172.36/44.05 #rules: 1 172.36/44.05 #arcs: 3/9 172.36/44.05 DPs: 172.36/44.05 b#(b(c(x1))) -> b#(x1) 172.36/44.05 TRS: 172.36/44.05 a(x1) -> b(c(b(x1))) 172.36/44.05 b(b(c(x1))) -> c(a(b(x1))) 172.36/44.05 c(c(x1)) -> x1 172.36/44.05 Usable Rule Processor: 172.36/44.05 DPs: 172.36/44.05 b#(b(c(x1))) -> b#(x1) 172.36/44.05 TRS: 172.36/44.05 172.36/44.05 Arctic Interpretation Processor: 172.36/44.05 dimension: 1 172.36/44.05 usable rules: 172.36/44.05 172.36/44.05 interpretation: 172.36/44.05 [b#](x0) = 6x0, 172.36/44.05 172.36/44.05 [c](x0) = x0 + 9, 172.36/44.05 172.36/44.05 [b](x0) = 1x0 + 12 172.36/44.05 orientation: 172.36/44.05 b#(b(c(x1))) = 7x1 + 18 >= 6x1 = b#(x1) 172.36/44.05 problem: 172.36/44.05 DPs: 172.36/44.05 172.36/44.05 TRS: 172.36/44.05 172.36/44.05 Qed 172.36/44.06 EOF