175.80/44.92 YES 175.80/44.93 175.80/44.93 Problem: 175.80/44.93 a(x1) -> b(c(x1)) 175.80/44.93 b(b(x1)) -> x1 175.80/44.93 b(c(c(x1))) -> c(c(a(b(x1)))) 175.80/44.93 175.80/44.93 Proof: 175.80/44.93 String Reversal Processor: 175.80/44.93 a(x1) -> c(b(x1)) 175.80/44.93 b(b(x1)) -> x1 175.80/44.93 c(c(b(x1))) -> b(a(c(c(x1)))) 175.80/44.93 DP Processor: 175.80/44.93 DPs: 175.80/44.93 a#(x1) -> b#(x1) 175.80/44.93 a#(x1) -> c#(b(x1)) 175.80/44.93 c#(c(b(x1))) -> c#(x1) 175.80/44.93 c#(c(b(x1))) -> c#(c(x1)) 175.80/44.93 c#(c(b(x1))) -> a#(c(c(x1))) 175.80/44.93 c#(c(b(x1))) -> b#(a(c(c(x1)))) 175.80/44.93 TRS: 175.80/44.93 a(x1) -> c(b(x1)) 175.80/44.93 b(b(x1)) -> x1 175.80/44.93 c(c(b(x1))) -> b(a(c(c(x1)))) 175.80/44.93 TDG Processor: 175.80/44.93 DPs: 175.80/44.93 a#(x1) -> b#(x1) 175.80/44.93 a#(x1) -> c#(b(x1)) 175.80/44.93 c#(c(b(x1))) -> c#(x1) 175.80/44.93 c#(c(b(x1))) -> c#(c(x1)) 175.80/44.93 c#(c(b(x1))) -> a#(c(c(x1))) 175.80/44.93 c#(c(b(x1))) -> b#(a(c(c(x1)))) 175.80/44.93 TRS: 175.80/44.93 a(x1) -> c(b(x1)) 175.80/44.93 b(b(x1)) -> x1 175.80/44.93 c(c(b(x1))) -> b(a(c(c(x1)))) 175.80/44.93 graph: 175.80/44.93 c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> b#(a(c(c(x1)))) 175.80/44.93 c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> a#(c(c(x1))) 175.80/44.93 c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> c#(c(x1)) 175.80/44.93 c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> c#(x1) 175.80/44.93 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> b#(a(c(c(x1)))) 175.80/44.93 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> a#(c(c(x1))) 175.80/44.93 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(c(x1)) 175.80/44.93 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(x1) 175.80/44.93 c#(c(b(x1))) -> a#(c(c(x1))) -> a#(x1) -> c#(b(x1)) 175.80/44.93 c#(c(b(x1))) -> a#(c(c(x1))) -> a#(x1) -> b#(x1) 175.80/44.93 a#(x1) -> c#(b(x1)) -> c#(c(b(x1))) -> b#(a(c(c(x1)))) 175.80/44.93 a#(x1) -> c#(b(x1)) -> c#(c(b(x1))) -> a#(c(c(x1))) 175.80/44.93 a#(x1) -> c#(b(x1)) -> c#(c(b(x1))) -> c#(c(x1)) 175.80/44.93 a#(x1) -> c#(b(x1)) -> c#(c(b(x1))) -> c#(x1) 175.80/44.93 SCC Processor: 175.80/44.93 #sccs: 1 175.80/44.93 #rules: 4 175.80/44.93 #arcs: 14/36 175.80/44.93 DPs: 175.80/44.93 c#(c(b(x1))) -> c#(c(x1)) 175.80/44.93 c#(c(b(x1))) -> c#(x1) 175.80/44.93 c#(c(b(x1))) -> a#(c(c(x1))) 175.80/44.93 a#(x1) -> c#(b(x1)) 175.80/44.93 TRS: 175.80/44.93 a(x1) -> c(b(x1)) 175.80/44.93 b(b(x1)) -> x1 175.80/44.93 c(c(b(x1))) -> b(a(c(c(x1)))) 175.80/44.93 Arctic Interpretation Processor: 175.80/44.93 dimension: 2 175.80/44.93 usable rules: 175.80/44.93 a(x1) -> c(b(x1)) 175.80/44.93 b(b(x1)) -> x1 175.80/44.93 c(c(b(x1))) -> b(a(c(c(x1)))) 175.80/44.93 interpretation: 175.80/44.93 [c#](x0) = [1 0]x0, 175.80/44.93 175.80/44.93 [a#](x0) = [0 2]x0 + [3], 175.80/44.93 175.80/44.93 [-& 0 ] [0] 175.80/44.93 [b](x0) = [0 2 ]x0 + [3], 175.80/44.93 175.80/44.93 [-& 0 ] [1] 175.80/44.93 [c](x0) = [0 -&]x0 + [0], 175.80/44.93 175.80/44.93 [0 2 ] [3] 175.80/44.93 [a](x0) = [-& 0 ]x0 + [0] 175.80/44.93 orientation: 175.80/44.93 c#(c(b(x1))) = [1 3]x1 + [4] >= [0 1]x1 + [2] = c#(c(x1)) 175.80/44.93 175.80/44.93 c#(c(b(x1))) = [1 3]x1 + [4] >= [1 0]x1 = c#(x1) 175.80/44.93 175.80/44.93 c#(c(b(x1))) = [1 3]x1 + [4] >= [0 2]x1 + [3] = a#(c(c(x1))) 175.80/44.93 175.80/44.93 a#(x1) = [0 2]x1 + [3] >= [0 2]x1 + [3] = c#(b(x1)) 175.80/44.93 175.80/44.93 [0 2 ] [3] [0 2 ] [3] 175.80/44.93 a(x1) = [-& 0 ]x1 + [0] >= [-& 0 ]x1 + [0] = c(b(x1)) 175.80/44.93 175.80/44.93 [0 2] [3] 175.80/44.93 b(b(x1)) = [2 4]x1 + [5] >= x1 = x1 175.80/44.93 175.80/44.93 [-& 0 ] [1] [-& 0 ] [1] 175.80/44.93 c(c(b(x1))) = [0 2 ]x1 + [3] >= [0 2 ]x1 + [3] = b(a(c(c(x1)))) 175.80/44.93 problem: 175.80/44.93 DPs: 175.80/44.93 c#(c(b(x1))) -> c#(x1) 175.80/44.93 a#(x1) -> c#(b(x1)) 175.80/44.93 TRS: 175.80/44.93 a(x1) -> c(b(x1)) 175.80/44.93 b(b(x1)) -> x1 175.80/44.93 c(c(b(x1))) -> b(a(c(c(x1)))) 175.80/44.93 Restore Modifier: 175.80/44.93 DPs: 175.80/44.93 c#(c(b(x1))) -> c#(x1) 175.80/44.93 a#(x1) -> c#(b(x1)) 175.80/44.93 TRS: 175.80/44.93 a(x1) -> c(b(x1)) 175.80/44.93 b(b(x1)) -> x1 175.80/44.93 c(c(b(x1))) -> b(a(c(c(x1)))) 175.80/44.93 EDG Processor: 175.80/44.93 DPs: 175.80/44.93 c#(c(b(x1))) -> c#(x1) 175.80/44.93 a#(x1) -> c#(b(x1)) 175.80/44.93 TRS: 175.80/44.93 a(x1) -> c(b(x1)) 175.80/44.93 b(b(x1)) -> x1 175.80/44.93 c(c(b(x1))) -> b(a(c(c(x1)))) 175.80/44.93 graph: 175.80/44.93 c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(x1) 175.80/44.93 a#(x1) -> c#(b(x1)) -> c#(c(b(x1))) -> c#(x1) 175.80/44.93 SCC Processor: 175.80/44.93 #sccs: 1 175.80/44.93 #rules: 1 175.80/44.93 #arcs: 2/4 175.80/44.93 DPs: 175.80/44.93 c#(c(b(x1))) -> c#(x1) 175.80/44.93 TRS: 175.80/44.93 a(x1) -> c(b(x1)) 175.80/44.93 b(b(x1)) -> x1 175.80/44.93 c(c(b(x1))) -> b(a(c(c(x1)))) 175.80/44.93 Usable Rule Processor: 175.80/44.93 DPs: 175.80/44.93 c#(c(b(x1))) -> c#(x1) 175.80/44.93 TRS: 175.80/44.93 175.80/44.93 Arctic Interpretation Processor: 175.80/44.93 dimension: 1 175.80/44.93 usable rules: 175.80/44.93 175.80/44.93 interpretation: 175.80/44.93 [c#](x0) = 6x0, 175.80/44.93 175.80/44.93 [b](x0) = x0 + 9, 175.80/44.93 175.80/44.93 [c](x0) = 1x0 + 12 175.80/44.93 orientation: 175.80/44.93 c#(c(b(x1))) = 7x1 + 18 >= 6x1 = c#(x1) 175.80/44.93 problem: 175.80/44.93 DPs: 175.80/44.93 175.80/44.93 TRS: 175.80/44.93 175.80/44.93 Qed 175.80/44.94 EOF