175.82/44.93 YES 175.84/44.94 175.84/44.94 Problem: 175.84/44.94 a(x1) -> x1 175.84/44.94 b(b(x1)) -> a(x1) 175.84/44.94 b(c(c(x1))) -> c(c(b(c(b(x1))))) 175.84/44.94 175.84/44.94 Proof: 175.84/44.94 String Reversal Processor: 175.84/44.94 a(x1) -> x1 175.84/44.94 b(b(x1)) -> a(x1) 175.84/44.94 c(c(b(x1))) -> b(c(b(c(c(x1))))) 175.84/44.94 DP Processor: 175.84/44.94 DPs: 175.84/44.94 b#(b(x1)) -> a#(x1) 175.84/44.94 c#(c(b(x1))) -> c#(x1) 175.84/44.94 c#(c(b(x1))) -> c#(c(x1)) 175.84/44.94 c#(c(b(x1))) -> b#(c(c(x1))) 175.84/44.94 c#(c(b(x1))) -> c#(b(c(c(x1)))) 175.84/44.94 c#(c(b(x1))) -> b#(c(b(c(c(x1))))) 175.84/44.94 TRS: 175.84/44.94 a(x1) -> x1 175.84/44.94 b(b(x1)) -> a(x1) 175.84/44.94 c(c(b(x1))) -> b(c(b(c(c(x1))))) 175.84/44.94 TDG Processor: 175.84/44.94 DPs: 175.84/44.94 b#(b(x1)) -> a#(x1) 175.84/44.94 c#(c(b(x1))) -> c#(x1) 175.84/44.94 c#(c(b(x1))) -> c#(c(x1)) 175.84/44.94 c#(c(b(x1))) -> b#(c(c(x1))) 175.84/44.94 c#(c(b(x1))) -> c#(b(c(c(x1)))) 175.84/44.94 c#(c(b(x1))) -> b#(c(b(c(c(x1))))) 175.84/44.94 TRS: 175.84/44.94 a(x1) -> x1 175.84/44.94 b(b(x1)) -> a(x1) 175.84/44.94 c(c(b(x1))) -> b(c(b(c(c(x1))))) 175.84/44.94 graph: 175.84/44.94 c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> b#(c(b(c(c(x1))))) 175.84/44.94 c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> c#(b(c(c(x1)))) 175.84/44.94 c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> b#(c(c(x1))) 175.84/44.94 c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> c#(c(x1)) 175.84/44.94 c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> c#(x1) 175.84/44.94 c#(c(b(x1))) -> c#(b(c(c(x1)))) -> 175.84/44.94 c#(c(b(x1))) -> b#(c(b(c(c(x1))))) 175.84/44.94 c#(c(b(x1))) -> c#(b(c(c(x1)))) -> 175.84/44.94 c#(c(b(x1))) -> c#(b(c(c(x1)))) 175.84/44.94 c#(c(b(x1))) -> c#(b(c(c(x1)))) -> c#(c(b(x1))) -> b#(c(c(x1))) 175.84/44.94 c#(c(b(x1))) -> c#(b(c(c(x1)))) -> c#(c(b(x1))) -> c#(c(x1)) 175.84/44.94 c#(c(b(x1))) -> c#(b(c(c(x1)))) -> c#(c(b(x1))) -> c#(x1) 175.84/44.94 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> b#(c(b(c(c(x1))))) 175.84/44.94 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(b(c(c(x1)))) 175.84/44.94 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> b#(c(c(x1))) 175.84/44.94 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(c(x1)) 175.84/44.94 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(x1) 175.84/44.94 c#(c(b(x1))) -> b#(c(c(x1))) -> b#(b(x1)) -> a#(x1) 175.84/44.94 c#(c(b(x1))) -> b#(c(b(c(c(x1))))) -> b#(b(x1)) -> a#(x1) 175.84/44.94 SCC Processor: 175.84/44.94 #sccs: 1 175.84/44.94 #rules: 3 175.84/44.94 #arcs: 17/36 175.84/44.94 DPs: 175.84/44.94 c#(c(b(x1))) -> c#(c(x1)) 175.84/44.94 c#(c(b(x1))) -> c#(x1) 175.84/44.94 c#(c(b(x1))) -> c#(b(c(c(x1)))) 175.84/44.94 TRS: 175.84/44.94 a(x1) -> x1 175.84/44.94 b(b(x1)) -> a(x1) 175.84/44.94 c(c(b(x1))) -> b(c(b(c(c(x1))))) 175.84/44.94 Arctic Interpretation Processor: 175.84/44.94 dimension: 2 175.84/44.94 usable rules: 175.84/44.94 a(x1) -> x1 175.84/44.94 b(b(x1)) -> a(x1) 175.84/44.94 c(c(b(x1))) -> b(c(b(c(c(x1))))) 175.84/44.94 interpretation: 175.84/44.94 [c#](x0) = [2 0]x0 + [0], 175.84/44.94 175.84/44.94 [-& 0 ] [1] 175.84/44.94 [c](x0) = [0 -&]x0 + [2], 175.84/44.94 175.84/44.94 [-& 0 ] [2] 175.84/44.94 [b](x0) = [0 1 ]x0 + [3], 175.84/44.94 175.84/44.94 [0 1] 175.84/44.94 [a](x0) = [1 2]x0 175.84/44.94 orientation: 175.84/44.94 c#(c(b(x1))) = [2 3]x1 + [5] >= [0 2]x1 + [3] = c#(c(x1)) 175.84/44.94 175.84/44.94 c#(c(b(x1))) = [2 3]x1 + [5] >= [2 0]x1 + [0] = c#(x1) 175.84/44.94 175.84/44.94 c#(c(b(x1))) = [2 3]x1 + [5] >= [0 2]x1 + [4] = c#(b(c(c(x1)))) 175.84/44.94 175.84/44.94 [0 1] 175.84/44.94 a(x1) = [1 2]x1 >= x1 = x1 175.84/44.94 175.84/44.94 [0 1] [3] [0 1] 175.84/44.94 b(b(x1)) = [1 2]x1 + [4] >= [1 2]x1 = a(x1) 175.84/44.94 175.84/44.94 [-& 0 ] [2] [-& 0 ] [2] 175.84/44.94 c(c(b(x1))) = [0 1 ]x1 + [3] >= [0 1 ]x1 + [3] = b(c(b(c(c(x1))))) 175.84/44.94 problem: 175.84/44.94 DPs: 175.84/44.94 c#(c(b(x1))) -> c#(x1) 175.84/44.94 TRS: 175.84/44.94 a(x1) -> x1 175.84/44.94 b(b(x1)) -> a(x1) 175.84/44.94 c(c(b(x1))) -> b(c(b(c(c(x1))))) 175.84/44.94 Restore Modifier: 175.84/44.94 DPs: 175.84/44.94 c#(c(b(x1))) -> c#(x1) 175.84/44.94 TRS: 175.84/44.94 a(x1) -> x1 175.84/44.94 b(b(x1)) -> a(x1) 175.84/44.94 c(c(b(x1))) -> b(c(b(c(c(x1))))) 175.84/44.94 EDG Processor: 175.84/44.94 DPs: 175.84/44.94 c#(c(b(x1))) -> c#(x1) 175.84/44.94 TRS: 175.84/44.94 a(x1) -> x1 175.84/44.94 b(b(x1)) -> a(x1) 175.84/44.94 c(c(b(x1))) -> b(c(b(c(c(x1))))) 175.84/44.94 graph: 175.84/44.94 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(x1) 175.84/44.94 Usable Rule Processor: 175.84/44.94 DPs: 175.84/44.94 c#(c(b(x1))) -> c#(x1) 175.84/44.94 TRS: 175.84/44.94 175.84/44.94 Arctic Interpretation Processor: 175.84/44.94 dimension: 1 175.84/44.94 usable rules: 175.84/44.94 175.84/44.94 interpretation: 175.84/44.94 [c#](x0) = 6x0, 175.84/44.94 175.84/44.94 [c](x0) = 1x0 + 12, 175.84/44.94 175.84/44.94 [b](x0) = x0 + 9 175.84/44.94 orientation: 175.84/44.94 c#(c(b(x1))) = 7x1 + 18 >= 6x1 = c#(x1) 175.84/44.94 problem: 175.84/44.94 DPs: 175.84/44.94 175.84/44.94 TRS: 175.84/44.94 175.84/44.94 Qed 175.84/44.94 EOF