186.54/47.70 YES 186.84/47.71 186.84/47.71 Problem: 186.84/47.71 a(x1) -> x1 186.84/47.71 a(b(x1)) -> b(a(a(c(x1)))) 186.84/47.71 b(x1) -> x1 186.84/47.71 c(c(a(x1))) -> b(x1) 186.84/47.71 186.84/47.71 Proof: 186.84/47.71 String Reversal Processor: 186.84/47.71 a(x1) -> x1 186.84/47.71 b(a(x1)) -> c(a(a(b(x1)))) 186.84/47.71 b(x1) -> x1 186.84/47.71 a(c(c(x1))) -> b(x1) 186.84/47.71 DP Processor: 186.84/47.71 DPs: 186.84/47.71 b#(a(x1)) -> b#(x1) 186.84/47.71 b#(a(x1)) -> a#(b(x1)) 186.84/47.71 b#(a(x1)) -> a#(a(b(x1))) 186.84/47.71 a#(c(c(x1))) -> b#(x1) 186.84/47.71 TRS: 186.84/47.71 a(x1) -> x1 186.84/47.71 b(a(x1)) -> c(a(a(b(x1)))) 186.84/47.71 b(x1) -> x1 186.84/47.71 a(c(c(x1))) -> b(x1) 186.84/47.71 TDG Processor: 186.84/47.71 DPs: 186.84/47.71 b#(a(x1)) -> b#(x1) 186.84/47.71 b#(a(x1)) -> a#(b(x1)) 186.84/47.71 b#(a(x1)) -> a#(a(b(x1))) 186.84/47.71 a#(c(c(x1))) -> b#(x1) 186.84/47.71 TRS: 186.84/47.71 a(x1) -> x1 186.84/47.71 b(a(x1)) -> c(a(a(b(x1)))) 186.84/47.71 b(x1) -> x1 186.84/47.71 a(c(c(x1))) -> b(x1) 186.84/47.71 graph: 186.84/47.71 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(a(b(x1))) 186.84/47.71 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(x1)) 186.84/47.71 b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1) 186.84/47.71 b#(a(x1)) -> a#(b(x1)) -> a#(c(c(x1))) -> b#(x1) 186.84/47.71 b#(a(x1)) -> a#(a(b(x1))) -> a#(c(c(x1))) -> b#(x1) 186.84/47.71 a#(c(c(x1))) -> b#(x1) -> b#(a(x1)) -> a#(a(b(x1))) 186.84/47.71 a#(c(c(x1))) -> b#(x1) -> b#(a(x1)) -> a#(b(x1)) 186.84/47.71 a#(c(c(x1))) -> b#(x1) -> b#(a(x1)) -> b#(x1) 186.84/47.71 Arctic Interpretation Processor: 186.84/47.71 dimension: 2 186.84/47.71 usable rules: 186.84/47.71 a(x1) -> x1 186.84/47.71 b(a(x1)) -> c(a(a(b(x1)))) 186.84/47.71 b(x1) -> x1 186.84/47.71 a(c(c(x1))) -> b(x1) 186.84/47.71 interpretation: 186.84/47.71 [b#](x0) = [0 2]x0 + [0], 186.84/47.71 186.84/47.71 [a#](x0) = [-& 2 ]x0 + [2], 186.84/47.71 186.84/47.71 [1 0 ] [0] 186.84/47.71 [c](x0) = [0 -&]x0 + [0], 186.84/47.71 186.84/47.71 [0 1 ] [0 ] 186.84/47.71 [b](x0) = [-& 0 ]x0 + [-&], 186.84/47.71 186.84/47.71 [0 0] [0] 186.84/47.71 [a](x0) = [0 1]x0 + [0] 186.84/47.71 orientation: 186.84/47.71 b#(a(x1)) = [2 3]x1 + [2] >= [0 2]x1 + [0] = b#(x1) 186.84/47.71 186.84/47.71 b#(a(x1)) = [2 3]x1 + [2] >= [-& 2 ]x1 + [2] = a#(b(x1)) 186.84/47.71 186.84/47.71 b#(a(x1)) = [2 3]x1 + [2] >= [2 3]x1 + [2] = a#(a(b(x1))) 186.84/47.71 186.84/47.71 a#(c(c(x1))) = [3 2]x1 + [2] >= [0 2]x1 + [0] = b#(x1) 186.84/47.71 186.84/47.71 [0 0] [0] 186.84/47.71 a(x1) = [0 1]x1 + [0] >= x1 = x1 186.84/47.71 186.84/47.71 [1 2] [1] [1 2] [1] 186.84/47.71 b(a(x1)) = [0 1]x1 + [0] >= [0 1]x1 + [0] = c(a(a(b(x1)))) 186.84/47.71 186.84/47.71 [0 1 ] [0 ] 186.84/47.71 b(x1) = [-& 0 ]x1 + [-&] >= x1 = x1 186.84/47.71 186.84/47.71 [2 1] [1] [0 1 ] [0 ] 186.84/47.71 a(c(c(x1))) = [2 1]x1 + [1] >= [-& 0 ]x1 + [-&] = b(x1) 186.84/47.71 problem: 186.84/47.71 DPs: 186.84/47.71 b#(a(x1)) -> a#(b(x1)) 186.84/47.71 b#(a(x1)) -> a#(a(b(x1))) 186.84/47.71 a#(c(c(x1))) -> b#(x1) 186.84/47.71 TRS: 186.84/47.71 a(x1) -> x1 186.84/47.71 b(a(x1)) -> c(a(a(b(x1)))) 186.84/47.71 b(x1) -> x1 186.84/47.71 a(c(c(x1))) -> b(x1) 186.84/47.71 Restore Modifier: 186.84/47.71 DPs: 186.84/47.71 b#(a(x1)) -> a#(b(x1)) 186.84/47.71 b#(a(x1)) -> a#(a(b(x1))) 186.84/47.71 a#(c(c(x1))) -> b#(x1) 186.84/47.71 TRS: 186.84/47.71 a(x1) -> x1 186.84/47.71 b(a(x1)) -> c(a(a(b(x1)))) 186.84/47.71 b(x1) -> x1 186.84/47.71 a(c(c(x1))) -> b(x1) 186.84/47.71 EDG Processor: 186.84/47.71 DPs: 186.84/47.71 b#(a(x1)) -> a#(b(x1)) 186.84/47.71 b#(a(x1)) -> a#(a(b(x1))) 186.84/47.71 a#(c(c(x1))) -> b#(x1) 186.84/47.71 TRS: 186.84/47.71 a(x1) -> x1 186.84/47.71 b(a(x1)) -> c(a(a(b(x1)))) 186.84/47.71 b(x1) -> x1 186.84/47.71 a(c(c(x1))) -> b(x1) 186.84/47.71 graph: 186.84/47.71 b#(a(x1)) -> a#(b(x1)) -> a#(c(c(x1))) -> b#(x1) 186.84/47.71 b#(a(x1)) -> a#(a(b(x1))) -> a#(c(c(x1))) -> b#(x1) 186.84/47.71 a#(c(c(x1))) -> b#(x1) -> b#(a(x1)) -> a#(b(x1)) 186.84/47.71 a#(c(c(x1))) -> b#(x1) -> b#(a(x1)) -> a#(a(b(x1))) 186.84/47.71 Arctic Interpretation Processor: 186.84/47.71 dimension: 2 186.84/47.71 usable rules: 186.84/47.71 a(x1) -> x1 186.84/47.71 b(a(x1)) -> c(a(a(b(x1)))) 186.84/47.71 b(x1) -> x1 186.84/47.71 a(c(c(x1))) -> b(x1) 186.84/47.71 interpretation: 186.84/47.71 [b#](x0) = [0 1]x0 + [2], 186.84/47.71 186.84/47.71 [a#](x0) = [0 0]x0 + [0], 186.84/47.71 186.84/47.71 [-& 0 ] [1] 186.84/47.71 [c](x0) = [0 1 ]x0 + [2], 186.84/47.71 186.84/47.71 [0 -&] [0] 186.84/47.71 [b](x0) = [1 0 ]x0 + [1], 186.84/47.71 186.84/47.71 [1 0] [1] 186.84/47.71 [a](x0) = [0 0]x0 + [0] 186.84/47.71 orientation: 186.84/47.71 b#(a(x1)) = [1 1]x1 + [2] >= [1 0]x1 + [1] = a#(b(x1)) 186.84/47.71 186.84/47.71 b#(a(x1)) = [1 1]x1 + [2] >= [1 0]x1 + [1] = a#(a(b(x1))) 186.84/47.71 186.84/47.71 a#(c(c(x1))) = [1 2]x1 + [3] >= [0 1]x1 + [2] = b#(x1) 186.84/47.71 186.84/47.71 [1 0] [1] 186.84/47.71 a(x1) = [0 0]x1 + [0] >= x1 = x1 186.84/47.71 186.84/47.71 [1 0] [1] [1 0] [1] 186.84/47.71 b(a(x1)) = [2 1]x1 + [2] >= [2 1]x1 + [2] = c(a(a(b(x1)))) 186.84/47.71 186.84/47.71 [0 -&] [0] 186.84/47.71 b(x1) = [1 0 ]x1 + [1] >= x1 = x1 186.84/47.71 186.84/47.71 [1 2] [3] [0 -&] [0] 186.84/47.71 a(c(c(x1))) = [1 2]x1 + [3] >= [1 0 ]x1 + [1] = b(x1) 186.84/47.71 problem: 186.84/47.71 DPs: 186.84/47.71 b#(a(x1)) -> a#(b(x1)) 186.84/47.71 b#(a(x1)) -> a#(a(b(x1))) 186.84/47.71 TRS: 186.84/47.71 a(x1) -> x1 186.84/47.71 b(a(x1)) -> c(a(a(b(x1)))) 186.84/47.71 b(x1) -> x1 186.84/47.71 a(c(c(x1))) -> b(x1) 186.84/47.71 Restore Modifier: 186.84/47.71 DPs: 186.84/47.71 b#(a(x1)) -> a#(b(x1)) 186.84/47.71 b#(a(x1)) -> a#(a(b(x1))) 186.84/47.71 TRS: 186.84/47.71 a(x1) -> x1 186.84/47.71 b(a(x1)) -> c(a(a(b(x1)))) 186.84/47.71 b(x1) -> x1 186.84/47.71 a(c(c(x1))) -> b(x1) 186.84/47.71 EDG Processor: 186.84/47.71 DPs: 186.84/47.71 b#(a(x1)) -> a#(b(x1)) 186.84/47.71 b#(a(x1)) -> a#(a(b(x1))) 186.84/47.71 TRS: 186.84/47.71 a(x1) -> x1 186.84/47.71 b(a(x1)) -> c(a(a(b(x1)))) 186.84/47.71 b(x1) -> x1 186.84/47.71 a(c(c(x1))) -> b(x1) 186.84/47.71 graph: 186.84/47.71 186.84/47.71 SCC Processor: 186.84/47.71 #sccs: 0 186.84/47.71 #rules: 0 186.84/47.71 #arcs: 0/4 186.84/47.71 186.84/47.71 EOF