168.37/43.14 YES 168.37/43.15 168.37/43.15 Problem: 168.37/43.15 c(c(c(a(x1)))) -> d(d(x1)) 168.37/43.15 d(b(x1)) -> c(c(x1)) 168.37/43.15 b(c(x1)) -> b(a(c(x1))) 168.37/43.15 c(x1) -> a(a(x1)) 168.37/43.15 d(x1) -> b(c(x1)) 168.37/43.15 168.37/43.15 Proof: 168.37/43.15 Matrix Interpretation Processor: dim=1 168.37/43.15 168.37/43.15 interpretation: 168.37/43.15 [b](x0) = x0 + 2, 168.37/43.15 168.37/43.15 [d](x0) = x0 + 6, 168.37/43.15 168.37/43.15 [c](x0) = x0 + 4, 168.37/43.15 168.37/43.15 [a](x0) = x0 168.37/43.15 orientation: 168.37/43.15 c(c(c(a(x1)))) = x1 + 12 >= x1 + 12 = d(d(x1)) 168.37/43.15 168.37/43.15 d(b(x1)) = x1 + 8 >= x1 + 8 = c(c(x1)) 168.37/43.15 168.37/43.15 b(c(x1)) = x1 + 6 >= x1 + 6 = b(a(c(x1))) 168.37/43.15 168.37/43.15 c(x1) = x1 + 4 >= x1 = a(a(x1)) 168.37/43.15 168.37/43.15 d(x1) = x1 + 6 >= x1 + 6 = b(c(x1)) 168.37/43.15 problem: 168.37/43.15 c(c(c(a(x1)))) -> d(d(x1)) 168.37/43.15 d(b(x1)) -> c(c(x1)) 168.37/43.15 b(c(x1)) -> b(a(c(x1))) 168.37/43.15 d(x1) -> b(c(x1)) 168.37/43.15 String Reversal Processor: 168.37/43.15 a(c(c(c(x1)))) -> d(d(x1)) 168.37/43.15 b(d(x1)) -> c(c(x1)) 168.37/43.15 c(b(x1)) -> c(a(b(x1))) 168.37/43.15 d(x1) -> c(b(x1)) 168.37/43.15 DP Processor: 168.37/43.15 DPs: 168.37/43.15 a#(c(c(c(x1)))) -> d#(x1) 168.37/43.15 a#(c(c(c(x1)))) -> d#(d(x1)) 168.37/43.15 b#(d(x1)) -> c#(x1) 168.37/43.15 b#(d(x1)) -> c#(c(x1)) 168.37/43.15 c#(b(x1)) -> a#(b(x1)) 168.37/43.15 c#(b(x1)) -> c#(a(b(x1))) 168.37/43.15 d#(x1) -> b#(x1) 168.37/43.15 d#(x1) -> c#(b(x1)) 168.37/43.15 TRS: 168.37/43.15 a(c(c(c(x1)))) -> d(d(x1)) 168.37/43.15 b(d(x1)) -> c(c(x1)) 168.37/43.15 c(b(x1)) -> c(a(b(x1))) 168.37/43.15 d(x1) -> c(b(x1)) 168.37/43.15 TDG Processor: 168.37/43.15 DPs: 168.37/43.15 a#(c(c(c(x1)))) -> d#(x1) 168.37/43.15 a#(c(c(c(x1)))) -> d#(d(x1)) 168.37/43.15 b#(d(x1)) -> c#(x1) 168.37/43.15 b#(d(x1)) -> c#(c(x1)) 168.37/43.15 c#(b(x1)) -> a#(b(x1)) 168.37/43.15 c#(b(x1)) -> c#(a(b(x1))) 168.37/43.15 d#(x1) -> b#(x1) 168.37/43.15 d#(x1) -> c#(b(x1)) 168.37/43.15 TRS: 168.37/43.15 a(c(c(c(x1)))) -> d(d(x1)) 168.37/43.15 b(d(x1)) -> c(c(x1)) 168.37/43.15 c(b(x1)) -> c(a(b(x1))) 168.37/43.15 d(x1) -> c(b(x1)) 168.37/43.15 graph: 168.37/43.15 c#(b(x1)) -> c#(a(b(x1))) -> c#(b(x1)) -> c#(a(b(x1))) 168.37/43.15 c#(b(x1)) -> c#(a(b(x1))) -> c#(b(x1)) -> a#(b(x1)) 168.37/43.15 c#(b(x1)) -> a#(b(x1)) -> a#(c(c(c(x1)))) -> d#(d(x1)) 168.37/43.15 c#(b(x1)) -> a#(b(x1)) -> a#(c(c(c(x1)))) -> d#(x1) 168.37/43.15 b#(d(x1)) -> c#(c(x1)) -> c#(b(x1)) -> c#(a(b(x1))) 168.37/43.15 b#(d(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(b(x1)) 168.37/43.15 b#(d(x1)) -> c#(x1) -> c#(b(x1)) -> c#(a(b(x1))) 168.37/43.15 b#(d(x1)) -> c#(x1) -> c#(b(x1)) -> a#(b(x1)) 168.37/43.15 d#(x1) -> c#(b(x1)) -> c#(b(x1)) -> c#(a(b(x1))) 168.37/43.15 d#(x1) -> c#(b(x1)) -> c#(b(x1)) -> a#(b(x1)) 168.37/43.15 d#(x1) -> b#(x1) -> b#(d(x1)) -> c#(c(x1)) 168.37/43.15 d#(x1) -> b#(x1) -> b#(d(x1)) -> c#(x1) 168.37/43.15 a#(c(c(c(x1)))) -> d#(d(x1)) -> d#(x1) -> c#(b(x1)) 168.37/43.15 a#(c(c(c(x1)))) -> d#(d(x1)) -> d#(x1) -> b#(x1) 168.37/43.15 a#(c(c(c(x1)))) -> d#(x1) -> d#(x1) -> c#(b(x1)) 168.37/43.15 a#(c(c(c(x1)))) -> d#(x1) -> d#(x1) -> b#(x1) 168.37/43.15 EDG Processor: 168.37/43.15 DPs: 168.37/43.15 a#(c(c(c(x1)))) -> d#(x1) 168.37/43.15 a#(c(c(c(x1)))) -> d#(d(x1)) 168.37/43.15 b#(d(x1)) -> c#(x1) 168.37/43.15 b#(d(x1)) -> c#(c(x1)) 168.37/43.15 c#(b(x1)) -> a#(b(x1)) 168.37/43.15 c#(b(x1)) -> c#(a(b(x1))) 168.37/43.15 d#(x1) -> b#(x1) 168.37/43.15 d#(x1) -> c#(b(x1)) 168.37/43.15 TRS: 168.37/43.15 a(c(c(c(x1)))) -> d(d(x1)) 168.37/43.15 b(d(x1)) -> c(c(x1)) 168.37/43.15 c(b(x1)) -> c(a(b(x1))) 168.37/43.15 d(x1) -> c(b(x1)) 168.37/43.15 graph: 168.37/43.15 c#(b(x1)) -> a#(b(x1)) -> a#(c(c(c(x1)))) -> d#(x1) 168.37/43.15 c#(b(x1)) -> a#(b(x1)) -> a#(c(c(c(x1)))) -> d#(d(x1)) 168.37/43.15 b#(d(x1)) -> c#(x1) -> c#(b(x1)) -> a#(b(x1)) 168.37/43.15 b#(d(x1)) -> c#(x1) -> c#(b(x1)) -> c#(a(b(x1))) 168.37/43.15 d#(x1) -> c#(b(x1)) -> c#(b(x1)) -> a#(b(x1)) 168.37/43.15 d#(x1) -> c#(b(x1)) -> c#(b(x1)) -> c#(a(b(x1))) 168.37/43.15 d#(x1) -> b#(x1) -> b#(d(x1)) -> c#(x1) 168.37/43.15 d#(x1) -> b#(x1) -> b#(d(x1)) -> c#(c(x1)) 168.37/43.15 a#(c(c(c(x1)))) -> d#(d(x1)) -> d#(x1) -> b#(x1) 168.37/43.15 a#(c(c(c(x1)))) -> d#(d(x1)) -> d#(x1) -> c#(b(x1)) 168.37/43.15 a#(c(c(c(x1)))) -> d#(x1) -> d#(x1) -> b#(x1) 168.37/43.15 a#(c(c(c(x1)))) -> d#(x1) -> d#(x1) -> c#(b(x1)) 168.37/43.15 SCC Processor: 168.37/43.15 #sccs: 1 168.37/43.15 #rules: 6 168.37/43.15 #arcs: 12/64 168.37/43.15 DPs: 168.37/43.15 c#(b(x1)) -> a#(b(x1)) 168.37/43.15 a#(c(c(c(x1)))) -> d#(d(x1)) 168.37/43.15 d#(x1) -> c#(b(x1)) 168.37/43.15 d#(x1) -> b#(x1) 168.37/43.15 b#(d(x1)) -> c#(x1) 168.37/43.15 a#(c(c(c(x1)))) -> d#(x1) 168.37/43.15 TRS: 168.37/43.15 a(c(c(c(x1)))) -> d(d(x1)) 168.37/43.15 b(d(x1)) -> c(c(x1)) 168.37/43.15 c(b(x1)) -> c(a(b(x1))) 168.37/43.15 d(x1) -> c(b(x1)) 168.37/43.15 Arctic Interpretation Processor: 168.37/43.15 dimension: 1 168.37/43.15 usable rules: 168.37/43.15 a(c(c(c(x1)))) -> d(d(x1)) 168.37/43.15 b(d(x1)) -> c(c(x1)) 168.37/43.15 c(b(x1)) -> c(a(b(x1))) 168.37/43.15 d(x1) -> c(b(x1)) 168.37/43.15 interpretation: 168.37/43.15 [c#](x0) = 4x0, 168.37/43.15 168.37/43.15 [b#](x0) = 1x0, 168.37/43.15 168.37/43.15 [d#](x0) = 8x0, 168.37/43.15 168.37/43.15 [a#](x0) = 1x0, 168.37/43.15 168.37/43.15 [b](x0) = 4x0, 168.37/43.15 168.37/43.15 [d](x0) = 12x0, 168.37/43.15 168.37/43.15 [c](x0) = 8x0, 168.37/43.15 168.37/43.15 [a](x0) = x0 168.37/43.15 orientation: 168.37/43.15 c#(b(x1)) = 8x1 >= 5x1 = a#(b(x1)) 168.37/43.15 168.37/43.15 a#(c(c(c(x1)))) = 25x1 >= 20x1 = d#(d(x1)) 168.37/43.15 168.37/43.15 d#(x1) = 8x1 >= 8x1 = c#(b(x1)) 168.37/43.15 168.37/43.15 d#(x1) = 8x1 >= 1x1 = b#(x1) 168.37/43.15 168.37/43.15 b#(d(x1)) = 13x1 >= 4x1 = c#(x1) 168.37/43.15 168.37/43.15 a#(c(c(c(x1)))) = 25x1 >= 8x1 = d#(x1) 168.37/43.15 168.37/43.15 a(c(c(c(x1)))) = 24x1 >= 24x1 = d(d(x1)) 168.37/43.15 168.37/43.15 b(d(x1)) = 16x1 >= 16x1 = c(c(x1)) 168.37/43.15 168.37/43.15 c(b(x1)) = 12x1 >= 12x1 = c(a(b(x1))) 168.37/43.15 168.37/43.15 d(x1) = 12x1 >= 12x1 = c(b(x1)) 168.37/43.15 problem: 168.37/43.15 DPs: 168.37/43.15 d#(x1) -> c#(b(x1)) 168.37/43.15 TRS: 168.37/43.15 a(c(c(c(x1)))) -> d(d(x1)) 168.37/43.15 b(d(x1)) -> c(c(x1)) 168.37/43.15 c(b(x1)) -> c(a(b(x1))) 168.37/43.15 d(x1) -> c(b(x1)) 168.37/43.15 Restore Modifier: 168.37/43.15 DPs: 168.37/43.15 d#(x1) -> c#(b(x1)) 168.37/43.15 TRS: 168.37/43.15 a(c(c(c(x1)))) -> d(d(x1)) 168.37/43.15 b(d(x1)) -> c(c(x1)) 168.37/43.15 c(b(x1)) -> c(a(b(x1))) 168.37/43.15 d(x1) -> c(b(x1)) 168.37/43.15 EDG Processor: 168.37/43.15 DPs: 168.37/43.15 d#(x1) -> c#(b(x1)) 168.37/43.15 TRS: 168.37/43.15 a(c(c(c(x1)))) -> d(d(x1)) 168.37/43.15 b(d(x1)) -> c(c(x1)) 168.37/43.15 c(b(x1)) -> c(a(b(x1))) 168.37/43.15 d(x1) -> c(b(x1)) 168.37/43.15 graph: 168.37/43.15 168.37/43.15 SCC Processor: 168.37/43.15 #sccs: 0 168.37/43.15 #rules: 0 168.37/43.15 #arcs: 0/1 168.37/43.15 168.37/43.16 EOF