178.86/45.73 YES 178.86/45.74 178.86/45.74 Problem: 178.86/45.74 a(a(x1)) -> b(a(c(x1))) 178.86/45.74 b(b(x1)) -> a(a(x1)) 178.86/45.74 c(b(x1)) -> a(x1) 178.86/45.74 178.86/45.74 Proof: 178.86/45.74 DP Processor: 178.86/45.74 DPs: 178.86/45.74 a#(a(x1)) -> c#(x1) 178.86/45.74 a#(a(x1)) -> a#(c(x1)) 178.86/45.74 a#(a(x1)) -> b#(a(c(x1))) 178.86/45.74 b#(b(x1)) -> a#(x1) 178.86/45.74 b#(b(x1)) -> a#(a(x1)) 178.86/45.74 c#(b(x1)) -> a#(x1) 178.86/45.74 TRS: 178.86/45.74 a(a(x1)) -> b(a(c(x1))) 178.86/45.74 b(b(x1)) -> a(a(x1)) 178.86/45.74 c(b(x1)) -> a(x1) 178.86/45.74 TDG Processor: 178.86/45.74 DPs: 178.86/45.74 a#(a(x1)) -> c#(x1) 178.86/45.74 a#(a(x1)) -> a#(c(x1)) 178.86/45.74 a#(a(x1)) -> b#(a(c(x1))) 178.86/45.74 b#(b(x1)) -> a#(x1) 178.86/45.74 b#(b(x1)) -> a#(a(x1)) 178.86/45.74 c#(b(x1)) -> a#(x1) 178.86/45.74 TRS: 178.86/45.74 a(a(x1)) -> b(a(c(x1))) 178.86/45.74 b(b(x1)) -> a(a(x1)) 178.86/45.74 c(b(x1)) -> a(x1) 178.86/45.74 graph: 178.86/45.74 b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> b#(a(c(x1))) 178.86/45.74 b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> a#(c(x1)) 178.86/45.74 b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> c#(x1) 178.86/45.74 b#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(c(x1))) 178.86/45.74 b#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(c(x1)) 178.86/45.74 b#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(x1) 178.86/45.74 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(c(x1))) 178.86/45.74 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(c(x1)) 178.86/45.74 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(x1) 178.86/45.74 a#(a(x1)) -> b#(a(c(x1))) -> b#(b(x1)) -> a#(a(x1)) 178.86/45.74 a#(a(x1)) -> b#(a(c(x1))) -> b#(b(x1)) -> a#(x1) 178.86/45.74 a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(x1) 178.86/45.74 a#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(a(c(x1))) 178.86/45.74 a#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(c(x1)) 178.86/45.74 a#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(x1) 178.86/45.74 Arctic Interpretation Processor: 178.86/45.74 dimension: 1 178.86/45.74 usable rules: 178.86/45.74 a(a(x1)) -> b(a(c(x1))) 178.86/45.74 b(b(x1)) -> a(a(x1)) 178.86/45.74 c(b(x1)) -> a(x1) 178.86/45.74 interpretation: 178.86/45.74 [b#](x0) = 3x0, 178.86/45.74 178.86/45.74 [c#](x0) = 4x0, 178.86/45.74 178.86/45.74 [a#](x0) = 3x0, 178.86/45.74 178.86/45.74 [b](x0) = 1x0, 178.86/45.74 178.86/45.74 [c](x0) = x0, 178.86/45.74 178.86/45.74 [a](x0) = 1x0 178.86/45.74 orientation: 178.86/45.74 a#(a(x1)) = 4x1 >= 4x1 = c#(x1) 178.86/45.74 178.86/45.74 a#(a(x1)) = 4x1 >= 3x1 = a#(c(x1)) 178.86/45.74 178.86/45.74 a#(a(x1)) = 4x1 >= 4x1 = b#(a(c(x1))) 178.86/45.74 178.86/45.74 b#(b(x1)) = 4x1 >= 3x1 = a#(x1) 178.86/45.74 178.86/45.74 b#(b(x1)) = 4x1 >= 4x1 = a#(a(x1)) 178.86/45.74 178.86/45.74 c#(b(x1)) = 5x1 >= 3x1 = a#(x1) 178.86/45.74 178.86/45.74 a(a(x1)) = 2x1 >= 2x1 = b(a(c(x1))) 178.86/45.74 178.86/45.74 b(b(x1)) = 2x1 >= 2x1 = a(a(x1)) 178.86/45.74 178.86/45.74 c(b(x1)) = 1x1 >= 1x1 = a(x1) 178.86/45.74 problem: 178.86/45.74 DPs: 178.86/45.74 a#(a(x1)) -> c#(x1) 178.86/45.74 a#(a(x1)) -> b#(a(c(x1))) 178.86/45.74 b#(b(x1)) -> a#(a(x1)) 178.86/45.74 TRS: 178.86/45.74 a(a(x1)) -> b(a(c(x1))) 178.86/45.74 b(b(x1)) -> a(a(x1)) 178.86/45.74 c(b(x1)) -> a(x1) 178.86/45.74 Restore Modifier: 178.86/45.74 DPs: 178.86/45.74 a#(a(x1)) -> c#(x1) 178.86/45.74 a#(a(x1)) -> b#(a(c(x1))) 178.86/45.74 b#(b(x1)) -> a#(a(x1)) 178.86/45.74 TRS: 178.86/45.74 a(a(x1)) -> b(a(c(x1))) 178.86/45.74 b(b(x1)) -> a(a(x1)) 178.86/45.74 c(b(x1)) -> a(x1) 178.86/45.74 EDG Processor: 178.86/45.74 DPs: 178.86/45.74 a#(a(x1)) -> c#(x1) 178.86/45.74 a#(a(x1)) -> b#(a(c(x1))) 178.86/45.74 b#(b(x1)) -> a#(a(x1)) 178.86/45.74 TRS: 178.86/45.74 a(a(x1)) -> b(a(c(x1))) 178.86/45.74 b(b(x1)) -> a(a(x1)) 178.86/45.74 c(b(x1)) -> a(x1) 178.86/45.74 graph: 178.86/45.74 b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> c#(x1) 178.86/45.74 b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> b#(a(c(x1))) 178.86/45.74 a#(a(x1)) -> b#(a(c(x1))) -> b#(b(x1)) -> a#(a(x1)) 178.86/45.74 SCC Processor: 178.86/45.74 #sccs: 1 178.86/45.74 #rules: 2 178.86/45.74 #arcs: 3/9 178.86/45.74 DPs: 178.86/45.74 b#(b(x1)) -> a#(a(x1)) 178.86/45.74 a#(a(x1)) -> b#(a(c(x1))) 178.86/45.74 TRS: 178.86/45.74 a(a(x1)) -> b(a(c(x1))) 178.86/45.74 b(b(x1)) -> a(a(x1)) 178.86/45.74 c(b(x1)) -> a(x1) 178.86/45.74 Arctic Interpretation Processor: 178.86/45.74 dimension: 2 178.86/45.74 usable rules: 178.86/45.74 a(a(x1)) -> b(a(c(x1))) 178.86/45.74 b(b(x1)) -> a(a(x1)) 178.86/45.74 c(b(x1)) -> a(x1) 178.86/45.74 interpretation: 178.86/45.74 [b#](x0) = [1 0]x0 + [0], 178.86/45.74 178.86/45.74 [a#](x0) = [-& 1 ]x0 + [0], 178.86/45.74 178.86/45.74 [1 0] [2] 178.86/45.74 [b](x0) = [1 0]x0 + [0], 178.86/45.74 178.86/45.74 [0 -&] 178.86/45.74 [c](x0) = [0 -&]x0, 178.86/45.74 178.86/45.74 [0 0] [-&] 178.86/45.74 [a](x0) = [1 0]x0 + [2 ] 178.86/45.74 orientation: 178.86/45.74 b#(b(x1)) = [2 1]x1 + [3] >= [2 1]x1 + [3] = a#(a(x1)) 178.86/45.74 178.86/45.74 a#(a(x1)) = [2 1]x1 + [3] >= [1 -&]x1 + [2] = b#(a(c(x1))) 178.86/45.74 178.86/45.74 [1 0] [2] [1 -&] [2] 178.86/45.74 a(a(x1)) = [1 1]x1 + [2] >= [1 -&]x1 + [2] = b(a(c(x1))) 178.86/45.74 178.86/45.74 [2 1] [3] [1 0] [2] 178.86/45.74 b(b(x1)) = [2 1]x1 + [3] >= [1 1]x1 + [2] = a(a(x1)) 178.86/45.74 178.86/45.74 [1 0] [2] [0 0] [-&] 178.86/45.74 c(b(x1)) = [1 0]x1 + [2] >= [1 0]x1 + [2 ] = a(x1) 178.86/45.74 problem: 178.86/45.74 DPs: 178.86/45.74 b#(b(x1)) -> a#(a(x1)) 178.86/45.74 TRS: 178.86/45.74 a(a(x1)) -> b(a(c(x1))) 178.86/45.74 b(b(x1)) -> a(a(x1)) 178.86/45.74 c(b(x1)) -> a(x1) 178.86/45.74 Restore Modifier: 178.86/45.74 DPs: 178.86/45.74 b#(b(x1)) -> a#(a(x1)) 178.86/45.74 TRS: 178.86/45.74 a(a(x1)) -> b(a(c(x1))) 178.86/45.74 b(b(x1)) -> a(a(x1)) 178.86/45.74 c(b(x1)) -> a(x1) 178.86/45.74 EDG Processor: 178.86/45.74 DPs: 178.86/45.74 b#(b(x1)) -> a#(a(x1)) 178.86/45.74 TRS: 178.86/45.74 a(a(x1)) -> b(a(c(x1))) 178.86/45.74 b(b(x1)) -> a(a(x1)) 178.86/45.74 c(b(x1)) -> a(x1) 178.86/45.74 graph: 178.86/45.74 178.86/45.74 SCC Processor: 178.86/45.74 #sccs: 0 178.86/45.74 #rules: 0 178.86/45.74 #arcs: 0/1 178.86/45.74 178.86/45.74 EOF