174.30/44.51 YES 174.30/44.51 174.30/44.51 Problem: 174.30/44.51 a(x1) -> b(b(c(b(x1)))) 174.30/44.51 c(b(b(x1))) -> a(c(x1)) 174.30/44.51 c(c(x1)) -> x1 174.30/44.51 174.30/44.51 Proof: 174.30/44.51 String Reversal Processor: 174.30/44.51 a(x1) -> b(c(b(b(x1)))) 174.30/44.51 b(b(c(x1))) -> c(a(x1)) 174.30/44.51 c(c(x1)) -> x1 174.30/44.51 DP Processor: 174.30/44.51 DPs: 174.30/44.51 a#(x1) -> b#(x1) 174.30/44.51 a#(x1) -> b#(b(x1)) 174.30/44.51 a#(x1) -> c#(b(b(x1))) 174.30/44.51 a#(x1) -> b#(c(b(b(x1)))) 174.30/44.51 b#(b(c(x1))) -> a#(x1) 174.30/44.51 b#(b(c(x1))) -> c#(a(x1)) 174.30/44.51 TRS: 174.30/44.51 a(x1) -> b(c(b(b(x1)))) 174.30/44.51 b(b(c(x1))) -> c(a(x1)) 174.30/44.51 c(c(x1)) -> x1 174.30/44.51 TDG Processor: 174.30/44.51 DPs: 174.30/44.51 a#(x1) -> b#(x1) 174.30/44.51 a#(x1) -> b#(b(x1)) 174.30/44.51 a#(x1) -> c#(b(b(x1))) 174.30/44.51 a#(x1) -> b#(c(b(b(x1)))) 174.30/44.51 b#(b(c(x1))) -> a#(x1) 174.30/44.51 b#(b(c(x1))) -> c#(a(x1)) 174.30/44.51 TRS: 174.30/44.51 a(x1) -> b(c(b(b(x1)))) 174.30/44.51 b(b(c(x1))) -> c(a(x1)) 174.30/44.51 c(c(x1)) -> x1 174.30/44.51 graph: 174.30/44.51 b#(b(c(x1))) -> a#(x1) -> a#(x1) -> b#(c(b(b(x1)))) 174.30/44.51 b#(b(c(x1))) -> a#(x1) -> a#(x1) -> c#(b(b(x1))) 174.30/44.51 b#(b(c(x1))) -> a#(x1) -> a#(x1) -> b#(b(x1)) 174.30/44.51 b#(b(c(x1))) -> a#(x1) -> a#(x1) -> b#(x1) 174.30/44.51 a#(x1) -> b#(c(b(b(x1)))) -> b#(b(c(x1))) -> c#(a(x1)) 174.30/44.51 a#(x1) -> b#(c(b(b(x1)))) -> b#(b(c(x1))) -> a#(x1) 174.30/44.51 a#(x1) -> b#(b(x1)) -> b#(b(c(x1))) -> c#(a(x1)) 174.30/44.51 a#(x1) -> b#(b(x1)) -> b#(b(c(x1))) -> a#(x1) 174.30/44.51 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> c#(a(x1)) 174.30/44.51 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> a#(x1) 174.30/44.51 SCC Processor: 174.30/44.51 #sccs: 1 174.30/44.51 #rules: 4 174.30/44.51 #arcs: 10/36 174.30/44.51 DPs: 174.30/44.51 b#(b(c(x1))) -> a#(x1) 174.30/44.51 a#(x1) -> b#(x1) 174.30/44.51 a#(x1) -> b#(b(x1)) 174.30/44.51 a#(x1) -> b#(c(b(b(x1)))) 174.30/44.51 TRS: 174.30/44.51 a(x1) -> b(c(b(b(x1)))) 174.30/44.51 b(b(c(x1))) -> c(a(x1)) 174.30/44.51 c(c(x1)) -> x1 174.30/44.51 Arctic Interpretation Processor: 174.30/44.51 dimension: 2 174.30/44.51 usable rules: 174.30/44.51 a(x1) -> b(c(b(b(x1)))) 174.30/44.51 b(b(c(x1))) -> c(a(x1)) 174.30/44.51 c(c(x1)) -> x1 174.30/44.51 interpretation: 174.30/44.51 [b#](x0) = [0 2]x0 + [0], 174.30/44.51 174.30/44.51 [a#](x0) = [3 2]x0 + [3], 174.30/44.51 174.30/44.51 [1 0 ] [2 ] 174.30/44.51 [c](x0) = [0 -&]x0 + [-&], 174.30/44.51 174.30/44.51 [-& 0 ] [0] 174.30/44.51 [b](x0) = [0 -&]x0 + [0], 174.30/44.51 174.30/44.51 [0 -&] [0] 174.30/44.51 [a](x0) = [1 0 ]x0 + [2] 174.30/44.51 orientation: 174.30/44.51 b#(b(c(x1))) = [3 2]x1 + [4] >= [3 2]x1 + [3] = a#(x1) 174.30/44.51 174.30/44.51 a#(x1) = [3 2]x1 + [3] >= [0 2]x1 + [0] = b#(x1) 174.30/44.51 174.30/44.51 a#(x1) = [3 2]x1 + [3] >= [2 0]x1 + [2] = b#(b(x1)) 174.30/44.51 174.30/44.51 a#(x1) = [3 2]x1 + [3] >= [2 0]x1 + [2] = b#(c(b(b(x1)))) 174.30/44.51 174.30/44.51 [0 -&] [0] [0 -&] [0] 174.30/44.51 a(x1) = [1 0 ]x1 + [2] >= [1 0 ]x1 + [2] = b(c(b(b(x1)))) 174.30/44.51 174.30/44.51 [1 0 ] [2] [1 0 ] [2] 174.30/44.51 b(b(c(x1))) = [0 -&]x1 + [0] >= [0 -&]x1 + [0] = c(a(x1)) 174.30/44.51 174.30/44.51 [2 1] [3] 174.30/44.51 c(c(x1)) = [1 0]x1 + [2] >= x1 = x1 174.30/44.51 problem: 174.30/44.51 DPs: 174.30/44.51 b#(b(c(x1))) -> a#(x1) 174.30/44.51 a#(x1) -> b#(x1) 174.30/44.51 TRS: 174.30/44.51 a(x1) -> b(c(b(b(x1)))) 174.30/44.51 b(b(c(x1))) -> c(a(x1)) 174.30/44.51 c(c(x1)) -> x1 174.30/44.51 Restore Modifier: 174.30/44.51 DPs: 174.30/44.51 b#(b(c(x1))) -> a#(x1) 174.30/44.51 a#(x1) -> b#(x1) 174.30/44.51 TRS: 174.30/44.51 a(x1) -> b(c(b(b(x1)))) 174.30/44.51 b(b(c(x1))) -> c(a(x1)) 174.30/44.51 c(c(x1)) -> x1 174.30/44.51 EDG Processor: 174.30/44.51 DPs: 174.30/44.51 b#(b(c(x1))) -> a#(x1) 174.30/44.51 a#(x1) -> b#(x1) 174.30/44.51 TRS: 174.30/44.51 a(x1) -> b(c(b(b(x1)))) 174.30/44.51 b(b(c(x1))) -> c(a(x1)) 174.30/44.51 c(c(x1)) -> x1 174.30/44.51 graph: 174.30/44.51 b#(b(c(x1))) -> a#(x1) -> a#(x1) -> b#(x1) 174.30/44.51 a#(x1) -> b#(x1) -> b#(b(c(x1))) -> a#(x1) 174.30/44.51 Usable Rule Processor: 174.30/44.51 DPs: 174.30/44.51 b#(b(c(x1))) -> a#(x1) 174.30/44.51 a#(x1) -> b#(x1) 174.30/44.51 TRS: 174.30/44.51 174.30/44.51 Arctic Interpretation Processor: 174.30/44.51 dimension: 1 174.30/44.51 usable rules: 174.30/44.51 174.30/44.51 interpretation: 174.30/44.51 [b#](x0) = x0, 174.30/44.51 174.30/44.51 [a#](x0) = x0, 174.30/44.51 174.30/44.51 [c](x0) = 1x0, 174.30/44.51 174.30/44.51 [b](x0) = x0 174.30/44.51 orientation: 174.30/44.51 b#(b(c(x1))) = 1x1 >= x1 = a#(x1) 174.30/44.51 174.30/44.51 a#(x1) = x1 >= x1 = b#(x1) 174.30/44.51 problem: 174.30/44.51 DPs: 174.30/44.51 a#(x1) -> b#(x1) 174.30/44.51 TRS: 174.30/44.51 174.30/44.51 Restore Modifier: 174.30/44.51 DPs: 174.30/44.51 a#(x1) -> b#(x1) 174.30/44.51 TRS: 174.30/44.51 a(x1) -> b(c(b(b(x1)))) 174.30/44.51 b(b(c(x1))) -> c(a(x1)) 174.30/44.51 c(c(x1)) -> x1 174.30/44.51 EDG Processor: 174.30/44.51 DPs: 174.30/44.51 a#(x1) -> b#(x1) 174.30/44.51 TRS: 174.30/44.51 a(x1) -> b(c(b(b(x1)))) 174.30/44.51 b(b(c(x1))) -> c(a(x1)) 174.30/44.51 c(c(x1)) -> x1 174.30/44.51 graph: 174.30/44.51 174.30/44.51 SCC Processor: 174.30/44.51 #sccs: 0 174.30/44.51 #rules: 0 174.30/44.51 #arcs: 0/1 174.30/44.51 174.30/44.52 EOF