190.64/48.32 YES 190.64/48.33 190.64/48.33 Problem: 190.64/48.33 a(a(x1)) -> b(a(c(b(x1)))) 190.64/48.33 b(b(x1)) -> a(a(x1)) 190.64/48.33 c(a(x1)) -> x1 190.64/48.33 190.64/48.33 Proof: 190.64/48.33 DP Processor: 190.64/48.33 DPs: 190.64/48.33 a#(a(x1)) -> b#(x1) 190.64/48.33 a#(a(x1)) -> c#(b(x1)) 190.64/48.33 a#(a(x1)) -> a#(c(b(x1))) 190.64/48.33 a#(a(x1)) -> b#(a(c(b(x1)))) 190.64/48.33 b#(b(x1)) -> a#(x1) 190.64/48.33 b#(b(x1)) -> a#(a(x1)) 190.64/48.33 TRS: 190.64/48.33 a(a(x1)) -> b(a(c(b(x1)))) 190.64/48.33 b(b(x1)) -> a(a(x1)) 190.64/48.33 c(a(x1)) -> x1 190.64/48.33 TDG Processor: 190.64/48.33 DPs: 190.64/48.33 a#(a(x1)) -> b#(x1) 190.64/48.33 a#(a(x1)) -> c#(b(x1)) 190.64/48.33 a#(a(x1)) -> a#(c(b(x1))) 190.64/48.33 a#(a(x1)) -> b#(a(c(b(x1)))) 190.64/48.33 b#(b(x1)) -> a#(x1) 190.64/48.33 b#(b(x1)) -> a#(a(x1)) 190.64/48.33 TRS: 190.64/48.33 a(a(x1)) -> b(a(c(b(x1)))) 190.64/48.33 b(b(x1)) -> a(a(x1)) 190.64/48.33 c(a(x1)) -> x1 190.64/48.33 graph: 190.64/48.33 b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> b#(a(c(b(x1)))) 190.64/48.33 b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> a#(c(b(x1))) 190.64/48.33 b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> c#(b(x1)) 190.64/48.33 b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> b#(x1) 190.64/48.33 b#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(c(b(x1)))) 190.64/48.33 b#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(c(b(x1))) 190.64/48.33 b#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(b(x1)) 190.64/48.33 b#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(x1) 190.64/48.33 a#(a(x1)) -> b#(a(c(b(x1)))) -> b#(b(x1)) -> a#(a(x1)) 190.64/48.33 a#(a(x1)) -> b#(a(c(b(x1)))) -> b#(b(x1)) -> a#(x1) 190.64/48.33 a#(a(x1)) -> b#(x1) -> b#(b(x1)) -> a#(a(x1)) 190.64/48.33 a#(a(x1)) -> b#(x1) -> b#(b(x1)) -> a#(x1) 190.64/48.33 a#(a(x1)) -> a#(c(b(x1))) -> a#(a(x1)) -> b#(a(c(b(x1)))) 190.64/48.33 a#(a(x1)) -> a#(c(b(x1))) -> a#(a(x1)) -> a#(c(b(x1))) 190.64/48.33 a#(a(x1)) -> a#(c(b(x1))) -> a#(a(x1)) -> c#(b(x1)) 190.64/48.33 a#(a(x1)) -> a#(c(b(x1))) -> a#(a(x1)) -> b#(x1) 190.64/48.33 SCC Processor: 190.64/48.33 #sccs: 1 190.64/48.33 #rules: 5 190.64/48.33 #arcs: 16/36 190.64/48.33 DPs: 190.64/48.33 b#(b(x1)) -> a#(a(x1)) 190.64/48.33 a#(a(x1)) -> b#(x1) 190.64/48.33 b#(b(x1)) -> a#(x1) 190.64/48.33 a#(a(x1)) -> a#(c(b(x1))) 190.64/48.33 a#(a(x1)) -> b#(a(c(b(x1)))) 190.64/48.33 TRS: 190.64/48.33 a(a(x1)) -> b(a(c(b(x1)))) 190.64/48.33 b(b(x1)) -> a(a(x1)) 190.64/48.33 c(a(x1)) -> x1 190.64/48.33 Arctic Interpretation Processor: 190.64/48.33 dimension: 1 190.64/48.33 usable rules: 190.64/48.33 a(a(x1)) -> b(a(c(b(x1)))) 190.64/48.33 b(b(x1)) -> a(a(x1)) 190.64/48.33 c(a(x1)) -> x1 190.64/48.33 interpretation: 190.64/48.33 [b#](x0) = 8x0 + -16, 190.64/48.33 190.64/48.33 [a#](x0) = 8x0 + 0, 190.64/48.33 190.64/48.33 [c](x0) = -1x0 + 1, 190.64/48.33 190.64/48.33 [b](x0) = 1x0 + 8, 190.64/48.33 190.64/48.33 [a](x0) = 1x0 + 8 190.64/48.33 orientation: 190.64/48.33 b#(b(x1)) = 9x1 + 16 >= 9x1 + 16 = a#(a(x1)) 190.64/48.33 190.64/48.33 a#(a(x1)) = 9x1 + 16 >= 8x1 + -16 = b#(x1) 190.64/48.33 190.64/48.33 b#(b(x1)) = 9x1 + 16 >= 8x1 + 0 = a#(x1) 190.64/48.33 190.64/48.33 a#(a(x1)) = 9x1 + 16 >= 8x1 + 15 = a#(c(b(x1))) 190.64/48.33 190.64/48.33 a#(a(x1)) = 9x1 + 16 >= 9x1 + 16 = b#(a(c(b(x1)))) 190.64/48.33 190.64/48.33 a(a(x1)) = 2x1 + 9 >= 2x1 + 9 = b(a(c(b(x1)))) 190.64/48.33 190.64/48.33 b(b(x1)) = 2x1 + 9 >= 2x1 + 9 = a(a(x1)) 190.64/48.33 190.64/48.33 c(a(x1)) = x1 + 7 >= x1 = x1 190.64/48.33 problem: 190.64/48.33 DPs: 190.64/48.33 b#(b(x1)) -> a#(a(x1)) 190.64/48.33 a#(a(x1)) -> b#(a(c(b(x1)))) 190.64/48.33 TRS: 190.64/48.33 a(a(x1)) -> b(a(c(b(x1)))) 190.64/48.33 b(b(x1)) -> a(a(x1)) 190.64/48.33 c(a(x1)) -> x1 190.64/48.33 Restore Modifier: 190.64/48.33 DPs: 190.64/48.33 b#(b(x1)) -> a#(a(x1)) 190.64/48.33 a#(a(x1)) -> b#(a(c(b(x1)))) 190.64/48.33 TRS: 190.64/48.33 a(a(x1)) -> b(a(c(b(x1)))) 190.64/48.33 b(b(x1)) -> a(a(x1)) 190.64/48.33 c(a(x1)) -> x1 190.64/48.33 EDG Processor: 190.64/48.33 DPs: 190.64/48.33 b#(b(x1)) -> a#(a(x1)) 190.64/48.33 a#(a(x1)) -> b#(a(c(b(x1)))) 190.64/48.33 TRS: 190.64/48.33 a(a(x1)) -> b(a(c(b(x1)))) 190.64/48.33 b(b(x1)) -> a(a(x1)) 190.64/48.33 c(a(x1)) -> x1 190.64/48.33 graph: 190.64/48.33 b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> b#(a(c(b(x1)))) 190.64/48.33 a#(a(x1)) -> b#(a(c(b(x1)))) -> b#(b(x1)) -> a#(a(x1)) 190.64/48.33 Arctic Interpretation Processor: 190.64/48.33 dimension: 3 190.64/48.33 usable rules: 190.64/48.33 a(a(x1)) -> b(a(c(b(x1)))) 190.64/48.33 b(b(x1)) -> a(a(x1)) 190.64/48.33 c(a(x1)) -> x1 190.64/48.33 interpretation: 190.64/48.33 [b#](x0) = [-& 0 0 ]x0 + [0], 190.64/48.33 190.64/48.33 [a#](x0) = [0 0 0]x0 + [0], 190.64/48.33 190.64/48.33 [-& 0 -&] [0] 190.64/48.33 [c](x0) = [-& 0 -&]x0 + [0] 190.64/48.33 [-& 0 -&] [0], 190.64/48.33 190.64/48.33 [0 0 1 ] [0] 190.64/48.33 [b](x0) = [-& 0 0 ]x0 + [0] 190.64/48.33 [0 1 1 ] [1], 190.64/48.33 190.64/48.33 [0 1 1 ] [1] 190.64/48.33 [a](x0) = [0 0 0 ]x0 + [0] 190.64/48.33 [0 0 -&] [0] 190.64/48.33 orientation: 190.64/48.33 b#(b(x1)) = [0 1 1]x1 + [1] >= [0 1 1]x1 + [1] = a#(a(x1)) 190.64/48.33 190.64/48.33 a#(a(x1)) = [0 1 1]x1 + [1] >= [-& 0 0 ]x1 + [0] = b#(a(c(b(x1)))) 190.64/48.33 190.64/48.33 [1 1 1] [1] [-& 1 1 ] [1] 190.64/48.33 a(a(x1)) = [0 1 1]x1 + [1] >= [-& 0 0 ]x1 + [0] = b(a(c(b(x1)))) 190.64/48.33 [0 1 1] [1] [-& 1 1 ] [1] 190.64/48.33 190.64/48.33 [1 2 2] [2] [1 1 1] [1] 190.64/48.33 b(b(x1)) = [0 1 1]x1 + [1] >= [0 1 1]x1 + [1] = a(a(x1)) 190.64/48.33 [1 2 2] [2] [0 1 1] [1] 190.64/48.33 190.64/48.33 [0 0 0] [0] 190.64/48.33 c(a(x1)) = [0 0 0]x1 + [0] >= x1 = x1 190.64/48.33 [0 0 0] [0] 190.64/48.33 problem: 190.64/48.33 DPs: 190.64/48.33 b#(b(x1)) -> a#(a(x1)) 190.64/48.33 TRS: 190.64/48.33 a(a(x1)) -> b(a(c(b(x1)))) 190.64/48.33 b(b(x1)) -> a(a(x1)) 190.64/48.33 c(a(x1)) -> x1 190.64/48.33 Restore Modifier: 190.64/48.33 DPs: 190.64/48.33 b#(b(x1)) -> a#(a(x1)) 190.64/48.33 TRS: 190.64/48.33 a(a(x1)) -> b(a(c(b(x1)))) 190.64/48.33 b(b(x1)) -> a(a(x1)) 190.64/48.33 c(a(x1)) -> x1 190.64/48.33 EDG Processor: 190.64/48.33 DPs: 190.64/48.33 b#(b(x1)) -> a#(a(x1)) 190.64/48.33 TRS: 190.64/48.33 a(a(x1)) -> b(a(c(b(x1)))) 190.64/48.33 b(b(x1)) -> a(a(x1)) 190.64/48.33 c(a(x1)) -> x1 190.64/48.33 graph: 190.64/48.33 190.64/48.33 SCC Processor: 190.64/48.33 #sccs: 0 190.64/48.33 #rules: 0 190.64/48.33 #arcs: 0/1 190.64/48.33 190.64/48.34 EOF