171.38/43.96 YES 172.00/43.96 172.00/43.96 Problem: 172.00/43.96 a(a(x1)) -> c(b(x1)) 172.00/43.96 b(b(x1)) -> c(a(x1)) 172.00/43.96 c(c(x1)) -> b(a(x1)) 172.00/43.96 172.00/43.96 Proof: 172.00/43.96 DP Processor: 172.00/43.96 DPs: 172.00/43.96 a#(a(x1)) -> b#(x1) 172.00/43.96 a#(a(x1)) -> c#(b(x1)) 172.00/43.96 b#(b(x1)) -> a#(x1) 172.00/43.96 b#(b(x1)) -> c#(a(x1)) 172.00/43.96 c#(c(x1)) -> a#(x1) 172.00/43.96 c#(c(x1)) -> b#(a(x1)) 172.00/43.96 TRS: 172.00/43.96 a(a(x1)) -> c(b(x1)) 172.00/43.96 b(b(x1)) -> c(a(x1)) 172.00/43.96 c(c(x1)) -> b(a(x1)) 172.00/43.96 TDG Processor: 172.00/43.96 DPs: 172.00/43.96 a#(a(x1)) -> b#(x1) 172.00/43.96 a#(a(x1)) -> c#(b(x1)) 172.00/43.96 b#(b(x1)) -> a#(x1) 172.00/43.96 b#(b(x1)) -> c#(a(x1)) 172.00/43.96 c#(c(x1)) -> a#(x1) 172.00/43.96 c#(c(x1)) -> b#(a(x1)) 172.00/43.96 TRS: 172.00/43.96 a(a(x1)) -> c(b(x1)) 172.00/43.96 b(b(x1)) -> c(a(x1)) 172.00/43.96 c(c(x1)) -> b(a(x1)) 172.00/43.96 graph: 172.00/43.96 c#(c(x1)) -> b#(a(x1)) -> b#(b(x1)) -> c#(a(x1)) 172.00/43.96 c#(c(x1)) -> b#(a(x1)) -> b#(b(x1)) -> a#(x1) 172.00/43.96 c#(c(x1)) -> a#(x1) -> a#(a(x1)) -> c#(b(x1)) 172.00/43.96 c#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(x1) 172.00/43.96 b#(b(x1)) -> c#(a(x1)) -> c#(c(x1)) -> b#(a(x1)) 172.00/43.96 b#(b(x1)) -> c#(a(x1)) -> c#(c(x1)) -> a#(x1) 172.00/43.96 b#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(b(x1)) 172.00/43.96 b#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(x1) 172.00/43.96 a#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> b#(a(x1)) 172.00/43.96 a#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> a#(x1) 172.00/43.96 a#(a(x1)) -> b#(x1) -> b#(b(x1)) -> c#(a(x1)) 172.00/43.96 a#(a(x1)) -> b#(x1) -> b#(b(x1)) -> a#(x1) 172.00/43.96 Arctic Interpretation Processor: 172.00/43.96 dimension: 1 172.00/43.96 usable rules: 172.00/43.96 a(a(x1)) -> c(b(x1)) 172.00/43.96 b(b(x1)) -> c(a(x1)) 172.00/43.96 c(c(x1)) -> b(a(x1)) 172.00/43.96 interpretation: 172.00/43.96 [c#](x0) = x0 + 0, 172.00/43.96 172.00/43.96 [b#](x0) = x0 + 0, 172.00/43.96 172.00/43.96 [a#](x0) = 8x0 + 0, 172.00/43.96 172.00/43.96 [c](x0) = 8x0 + 0, 172.00/43.96 172.00/43.96 [b](x0) = 8x0 + 0, 172.00/43.96 172.00/43.96 [a](x0) = 8x0 + 0 172.00/43.96 orientation: 172.00/43.96 a#(a(x1)) = 16x1 + 8 >= x1 + 0 = b#(x1) 172.00/43.96 172.00/43.96 a#(a(x1)) = 16x1 + 8 >= 8x1 + 0 = c#(b(x1)) 172.00/43.96 172.00/43.96 b#(b(x1)) = 8x1 + 0 >= 8x1 + 0 = a#(x1) 172.00/43.96 172.00/43.96 b#(b(x1)) = 8x1 + 0 >= 8x1 + 0 = c#(a(x1)) 172.00/43.96 172.00/43.96 c#(c(x1)) = 8x1 + 0 >= 8x1 + 0 = a#(x1) 172.00/43.96 172.00/43.96 c#(c(x1)) = 8x1 + 0 >= 8x1 + 0 = b#(a(x1)) 172.00/43.96 172.00/43.96 a(a(x1)) = 16x1 + 8 >= 16x1 + 8 = c(b(x1)) 172.00/43.96 172.00/43.96 b(b(x1)) = 16x1 + 8 >= 16x1 + 8 = c(a(x1)) 172.00/43.96 172.00/43.96 c(c(x1)) = 16x1 + 8 >= 16x1 + 8 = b(a(x1)) 172.00/43.96 problem: 172.00/43.96 DPs: 172.00/43.96 b#(b(x1)) -> a#(x1) 172.00/43.96 b#(b(x1)) -> c#(a(x1)) 172.00/43.96 c#(c(x1)) -> a#(x1) 172.00/43.96 c#(c(x1)) -> b#(a(x1)) 172.00/43.96 TRS: 172.00/43.96 a(a(x1)) -> c(b(x1)) 172.00/43.96 b(b(x1)) -> c(a(x1)) 172.00/43.96 c(c(x1)) -> b(a(x1)) 172.00/43.96 Restore Modifier: 172.00/43.96 DPs: 172.00/43.96 b#(b(x1)) -> a#(x1) 172.00/43.96 b#(b(x1)) -> c#(a(x1)) 172.00/43.96 c#(c(x1)) -> a#(x1) 172.00/43.96 c#(c(x1)) -> b#(a(x1)) 172.00/43.96 TRS: 172.00/43.96 a(a(x1)) -> c(b(x1)) 172.00/43.96 b(b(x1)) -> c(a(x1)) 172.00/43.96 c(c(x1)) -> b(a(x1)) 172.00/43.96 EDG Processor: 172.00/43.96 DPs: 172.00/43.96 b#(b(x1)) -> a#(x1) 172.00/43.96 b#(b(x1)) -> c#(a(x1)) 172.00/43.96 c#(c(x1)) -> a#(x1) 172.00/43.96 c#(c(x1)) -> b#(a(x1)) 172.00/43.96 TRS: 172.00/43.96 a(a(x1)) -> c(b(x1)) 172.00/43.96 b(b(x1)) -> c(a(x1)) 172.00/43.96 c(c(x1)) -> b(a(x1)) 172.00/43.96 graph: 172.00/43.96 c#(c(x1)) -> b#(a(x1)) -> b#(b(x1)) -> a#(x1) 172.00/43.96 c#(c(x1)) -> b#(a(x1)) -> b#(b(x1)) -> c#(a(x1)) 172.00/43.96 b#(b(x1)) -> c#(a(x1)) -> c#(c(x1)) -> a#(x1) 172.00/43.96 b#(b(x1)) -> c#(a(x1)) -> c#(c(x1)) -> b#(a(x1)) 172.00/43.96 SCC Processor: 172.00/43.96 #sccs: 1 172.00/43.96 #rules: 2 172.00/43.96 #arcs: 4/16 172.00/43.96 DPs: 172.00/43.96 c#(c(x1)) -> b#(a(x1)) 172.00/43.96 b#(b(x1)) -> c#(a(x1)) 172.00/43.96 TRS: 172.00/43.96 a(a(x1)) -> c(b(x1)) 172.00/43.96 b(b(x1)) -> c(a(x1)) 172.00/43.96 c(c(x1)) -> b(a(x1)) 172.00/43.96 Arctic Interpretation Processor: 172.00/43.96 dimension: 2 172.00/43.96 usable rules: 172.00/43.96 a(a(x1)) -> c(b(x1)) 172.00/43.96 b(b(x1)) -> c(a(x1)) 172.00/43.96 c(c(x1)) -> b(a(x1)) 172.00/43.96 interpretation: 172.00/43.96 [c#](x0) = [-& 0 ]x0 + [3], 172.00/43.96 172.00/43.96 [b#](x0) = [-& 0 ]x0 + [0], 172.00/43.96 172.00/43.96 [0 0 ] [2] 172.00/43.96 [c](x0) = [1 -&]x0 + [0], 172.00/43.96 172.00/43.96 [-& 0 ] [0] 172.00/43.96 [b](x0) = [0 1 ]x0 + [3], 172.00/43.96 172.00/43.96 [0 1 ] [1] 172.00/43.96 [a](x0) = [0 -&]x0 + [2] 172.00/43.96 orientation: 172.00/43.96 c#(c(x1)) = [1 -&]x1 + [3] >= [0 -&]x1 + [2] = b#(a(x1)) 172.00/43.96 172.00/43.96 b#(b(x1)) = [0 1]x1 + [3] >= [0 -&]x1 + [3] = c#(a(x1)) 172.00/43.96 172.00/43.96 [1 1] [3] [0 1 ] [3] 172.00/43.96 a(a(x1)) = [0 1]x1 + [2] >= [-& 1 ]x1 + [1] = c(b(x1)) 172.00/43.96 172.00/43.96 [0 1] [3] [0 1] [2] 172.00/43.96 b(b(x1)) = [1 2]x1 + [4] >= [1 2]x1 + [2] = c(a(x1)) 172.00/43.96 172.00/43.96 [1 0] [2] [0 -&] [2] 172.00/43.96 c(c(x1)) = [1 1]x1 + [3] >= [1 1 ]x1 + [3] = b(a(x1)) 172.00/43.96 problem: 172.00/43.96 DPs: 172.00/43.96 b#(b(x1)) -> c#(a(x1)) 172.00/43.96 TRS: 172.00/43.96 a(a(x1)) -> c(b(x1)) 172.00/43.96 b(b(x1)) -> c(a(x1)) 172.00/43.96 c(c(x1)) -> b(a(x1)) 172.00/43.96 Restore Modifier: 172.00/43.96 DPs: 172.00/43.96 b#(b(x1)) -> c#(a(x1)) 172.00/43.96 TRS: 172.00/43.96 a(a(x1)) -> c(b(x1)) 172.00/43.96 b(b(x1)) -> c(a(x1)) 172.00/43.96 c(c(x1)) -> b(a(x1)) 172.00/43.96 EDG Processor: 172.00/43.96 DPs: 172.00/43.96 b#(b(x1)) -> c#(a(x1)) 172.00/43.96 TRS: 172.00/43.96 a(a(x1)) -> c(b(x1)) 172.00/43.96 b(b(x1)) -> c(a(x1)) 172.00/43.96 c(c(x1)) -> b(a(x1)) 172.00/43.96 graph: 172.00/43.96 172.00/43.96 SCC Processor: 172.00/43.96 #sccs: 0 172.00/43.96 #rules: 0 172.00/43.96 #arcs: 0/1 172.00/43.96 172.00/43.97 EOF