187.65/47.86 YES 187.65/47.87 187.65/47.87 Problem: 187.65/47.87 b(a(a(x1))) -> a(b(c(x1))) 187.65/47.87 c(a(x1)) -> a(c(x1)) 187.65/47.87 b(c(a(x1))) -> a(b(c(x1))) 187.65/47.87 c(b(x1)) -> d(x1) 187.65/47.87 d(x1) -> b(a(x1)) 187.65/47.87 a(d(x1)) -> d(a(x1)) 187.65/47.87 a(a(x1)) -> a(b(a(x1))) 187.65/47.87 187.65/47.87 Proof: 187.65/47.87 DP Processor: 187.65/47.87 DPs: 187.65/47.87 b#(a(a(x1))) -> c#(x1) 187.65/47.87 b#(a(a(x1))) -> b#(c(x1)) 187.65/47.87 b#(a(a(x1))) -> a#(b(c(x1))) 187.65/47.87 c#(a(x1)) -> c#(x1) 187.65/47.87 c#(a(x1)) -> a#(c(x1)) 187.65/47.87 b#(c(a(x1))) -> c#(x1) 187.65/47.87 b#(c(a(x1))) -> b#(c(x1)) 187.65/47.87 b#(c(a(x1))) -> a#(b(c(x1))) 187.65/47.87 c#(b(x1)) -> d#(x1) 187.65/47.87 d#(x1) -> a#(x1) 187.65/47.87 d#(x1) -> b#(a(x1)) 187.65/47.87 a#(d(x1)) -> a#(x1) 187.65/47.87 a#(d(x1)) -> d#(a(x1)) 187.65/47.87 a#(a(x1)) -> b#(a(x1)) 187.65/47.87 a#(a(x1)) -> a#(b(a(x1))) 187.65/47.87 TRS: 187.65/47.87 b(a(a(x1))) -> a(b(c(x1))) 187.65/47.87 c(a(x1)) -> a(c(x1)) 187.65/47.87 b(c(a(x1))) -> a(b(c(x1))) 187.65/47.87 c(b(x1)) -> d(x1) 187.65/47.87 d(x1) -> b(a(x1)) 187.65/47.87 a(d(x1)) -> d(a(x1)) 187.65/47.87 a(a(x1)) -> a(b(a(x1))) 187.65/47.87 TDG Processor: 187.65/47.87 DPs: 187.65/47.87 b#(a(a(x1))) -> c#(x1) 187.65/47.87 b#(a(a(x1))) -> b#(c(x1)) 187.65/47.87 b#(a(a(x1))) -> a#(b(c(x1))) 187.65/47.87 c#(a(x1)) -> c#(x1) 187.65/47.87 c#(a(x1)) -> a#(c(x1)) 187.65/47.87 b#(c(a(x1))) -> c#(x1) 187.65/47.87 b#(c(a(x1))) -> b#(c(x1)) 187.65/47.87 b#(c(a(x1))) -> a#(b(c(x1))) 187.65/47.87 c#(b(x1)) -> d#(x1) 187.65/47.87 d#(x1) -> a#(x1) 187.65/47.87 d#(x1) -> b#(a(x1)) 187.65/47.87 a#(d(x1)) -> a#(x1) 187.65/47.87 a#(d(x1)) -> d#(a(x1)) 187.65/47.87 a#(a(x1)) -> b#(a(x1)) 187.65/47.87 a#(a(x1)) -> a#(b(a(x1))) 187.65/47.87 TRS: 187.65/47.87 b(a(a(x1))) -> a(b(c(x1))) 187.65/47.87 c(a(x1)) -> a(c(x1)) 187.65/47.87 b(c(a(x1))) -> a(b(c(x1))) 187.65/47.87 c(b(x1)) -> d(x1) 187.65/47.87 d(x1) -> b(a(x1)) 187.65/47.87 a(d(x1)) -> d(a(x1)) 187.65/47.87 a(a(x1)) -> a(b(a(x1))) 187.65/47.87 graph: 187.65/47.87 d#(x1) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1))) 187.65/47.87 d#(x1) -> a#(x1) -> a#(a(x1)) -> b#(a(x1)) 187.65/47.87 d#(x1) -> a#(x1) -> a#(d(x1)) -> d#(a(x1)) 187.65/47.87 d#(x1) -> a#(x1) -> a#(d(x1)) -> a#(x1) 187.65/47.87 d#(x1) -> b#(a(x1)) -> b#(c(a(x1))) -> a#(b(c(x1))) 187.65/47.87 d#(x1) -> b#(a(x1)) -> b#(c(a(x1))) -> b#(c(x1)) 187.65/47.87 d#(x1) -> b#(a(x1)) -> b#(c(a(x1))) -> c#(x1) 187.65/47.87 d#(x1) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(c(x1))) 187.65/47.87 d#(x1) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(c(x1)) 187.65/47.87 d#(x1) -> b#(a(x1)) -> b#(a(a(x1))) -> c#(x1) 187.65/47.87 a#(d(x1)) -> d#(a(x1)) -> d#(x1) -> b#(a(x1)) 187.65/47.87 a#(d(x1)) -> d#(a(x1)) -> d#(x1) -> a#(x1) 187.65/47.87 a#(d(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1))) 187.65/47.87 a#(d(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(x1)) 187.65/47.87 a#(d(x1)) -> a#(x1) -> a#(d(x1)) -> d#(a(x1)) 187.65/47.87 a#(d(x1)) -> a#(x1) -> a#(d(x1)) -> a#(x1) 187.65/47.87 a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(x1))) 187.65/47.87 a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(a(x1)) 187.65/47.87 a#(a(x1)) -> a#(b(a(x1))) -> a#(d(x1)) -> d#(a(x1)) 187.65/47.87 a#(a(x1)) -> a#(b(a(x1))) -> a#(d(x1)) -> a#(x1) 187.65/47.87 a#(a(x1)) -> b#(a(x1)) -> b#(c(a(x1))) -> a#(b(c(x1))) 187.65/47.87 a#(a(x1)) -> b#(a(x1)) -> b#(c(a(x1))) -> b#(c(x1)) 187.65/47.87 a#(a(x1)) -> b#(a(x1)) -> b#(c(a(x1))) -> c#(x1) 187.65/47.87 a#(a(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(c(x1))) 187.65/47.87 a#(a(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(c(x1)) 187.65/47.87 a#(a(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> c#(x1) 187.65/47.87 c#(b(x1)) -> d#(x1) -> d#(x1) -> b#(a(x1)) 187.65/47.87 c#(b(x1)) -> d#(x1) -> d#(x1) -> a#(x1) 187.65/47.87 c#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(a(x1))) 187.65/47.87 c#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(a(x1)) 187.65/47.87 c#(a(x1)) -> a#(c(x1)) -> a#(d(x1)) -> d#(a(x1)) 187.65/47.87 c#(a(x1)) -> a#(c(x1)) -> a#(d(x1)) -> a#(x1) 187.65/47.87 c#(a(x1)) -> c#(x1) -> c#(b(x1)) -> d#(x1) 187.65/47.87 c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(c(x1)) 187.65/47.87 c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1) 187.65/47.87 b#(c(a(x1))) -> a#(b(c(x1))) -> a#(a(x1)) -> a#(b(a(x1))) 187.65/47.87 b#(c(a(x1))) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(a(x1)) 187.65/47.87 b#(c(a(x1))) -> a#(b(c(x1))) -> a#(d(x1)) -> d#(a(x1)) 187.65/47.87 b#(c(a(x1))) -> a#(b(c(x1))) -> a#(d(x1)) -> a#(x1) 187.65/47.87 b#(c(a(x1))) -> c#(x1) -> c#(b(x1)) -> d#(x1) 187.65/47.87 b#(c(a(x1))) -> c#(x1) -> c#(a(x1)) -> a#(c(x1)) 187.65/47.87 b#(c(a(x1))) -> c#(x1) -> c#(a(x1)) -> c#(x1) 187.65/47.87 b#(c(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> a#(b(c(x1))) 187.65/47.87 b#(c(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> b#(c(x1)) 187.65/47.87 b#(c(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> c#(x1) 187.65/47.87 b#(c(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> a#(b(c(x1))) 187.65/47.87 b#(c(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> b#(c(x1)) 187.65/47.87 b#(c(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> c#(x1) 187.65/47.87 b#(a(a(x1))) -> a#(b(c(x1))) -> a#(a(x1)) -> a#(b(a(x1))) 187.65/47.87 b#(a(a(x1))) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(a(x1)) 187.65/47.87 b#(a(a(x1))) -> a#(b(c(x1))) -> a#(d(x1)) -> d#(a(x1)) 187.92/47.88 b#(a(a(x1))) -> a#(b(c(x1))) -> a#(d(x1)) -> a#(x1) 187.92/47.88 b#(a(a(x1))) -> c#(x1) -> c#(b(x1)) -> d#(x1) 187.92/47.88 b#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> a#(c(x1)) 187.92/47.88 b#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> c#(x1) 187.92/47.88 b#(a(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> a#(b(c(x1))) 187.92/47.88 b#(a(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> b#(c(x1)) 187.92/47.88 b#(a(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> c#(x1) 187.92/47.88 b#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> a#(b(c(x1))) 187.92/47.88 b#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> b#(c(x1)) 187.92/47.88 b#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> c#(x1) 187.92/47.88 EDG Processor: 187.92/47.88 DPs: 187.92/47.88 b#(a(a(x1))) -> c#(x1) 187.92/47.88 b#(a(a(x1))) -> b#(c(x1)) 187.92/47.88 b#(a(a(x1))) -> a#(b(c(x1))) 187.92/47.88 c#(a(x1)) -> c#(x1) 187.92/47.88 c#(a(x1)) -> a#(c(x1)) 187.92/47.88 b#(c(a(x1))) -> c#(x1) 187.92/47.88 b#(c(a(x1))) -> b#(c(x1)) 187.92/47.88 b#(c(a(x1))) -> a#(b(c(x1))) 187.92/47.88 c#(b(x1)) -> d#(x1) 187.92/47.88 d#(x1) -> a#(x1) 187.92/47.88 d#(x1) -> b#(a(x1)) 187.92/47.88 a#(d(x1)) -> a#(x1) 187.92/47.88 a#(d(x1)) -> d#(a(x1)) 187.92/47.88 a#(a(x1)) -> b#(a(x1)) 187.92/47.88 a#(a(x1)) -> a#(b(a(x1))) 187.92/47.88 TRS: 187.92/47.88 b(a(a(x1))) -> a(b(c(x1))) 187.92/47.88 c(a(x1)) -> a(c(x1)) 187.92/47.88 b(c(a(x1))) -> a(b(c(x1))) 187.92/47.88 c(b(x1)) -> d(x1) 187.92/47.88 d(x1) -> b(a(x1)) 187.92/47.88 a(d(x1)) -> d(a(x1)) 187.92/47.88 a(a(x1)) -> a(b(a(x1))) 187.92/47.88 graph: 187.92/47.88 d#(x1) -> a#(x1) -> a#(d(x1)) -> a#(x1) 187.92/47.88 d#(x1) -> a#(x1) -> a#(d(x1)) -> d#(a(x1)) 187.92/47.88 d#(x1) -> a#(x1) -> a#(a(x1)) -> b#(a(x1)) 187.92/47.88 d#(x1) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1))) 187.92/47.88 d#(x1) -> b#(a(x1)) -> b#(a(a(x1))) -> c#(x1) 187.92/47.88 d#(x1) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(c(x1)) 187.92/47.88 d#(x1) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(c(x1))) 187.92/47.88 a#(d(x1)) -> d#(a(x1)) -> d#(x1) -> a#(x1) 187.92/47.88 a#(d(x1)) -> d#(a(x1)) -> d#(x1) -> b#(a(x1)) 187.92/47.88 a#(d(x1)) -> a#(x1) -> a#(d(x1)) -> a#(x1) 187.92/47.88 a#(d(x1)) -> a#(x1) -> a#(d(x1)) -> d#(a(x1)) 187.92/47.88 a#(d(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(x1)) 187.92/47.88 a#(d(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1))) 187.92/47.88 a#(a(x1)) -> a#(b(a(x1))) -> a#(d(x1)) -> a#(x1) 187.92/47.88 a#(a(x1)) -> a#(b(a(x1))) -> a#(d(x1)) -> d#(a(x1)) 187.92/47.88 a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(a(x1)) 187.92/47.88 a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(x1))) 187.92/47.88 a#(a(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> c#(x1) 187.92/47.88 a#(a(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(c(x1)) 187.92/47.88 a#(a(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(c(x1))) 187.92/47.88 c#(b(x1)) -> d#(x1) -> d#(x1) -> a#(x1) 187.92/47.88 c#(b(x1)) -> d#(x1) -> d#(x1) -> b#(a(x1)) 187.92/47.88 c#(a(x1)) -> a#(c(x1)) -> a#(d(x1)) -> a#(x1) 187.92/47.88 c#(a(x1)) -> a#(c(x1)) -> a#(d(x1)) -> d#(a(x1)) 187.92/47.88 c#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(a(x1)) 187.92/47.88 c#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(a(x1))) 187.92/47.88 c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1) 187.92/47.88 c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(c(x1)) 187.92/47.88 c#(a(x1)) -> c#(x1) -> c#(b(x1)) -> d#(x1) 187.92/47.88 b#(c(a(x1))) -> a#(b(c(x1))) -> a#(d(x1)) -> a#(x1) 187.92/47.88 b#(c(a(x1))) -> a#(b(c(x1))) -> a#(d(x1)) -> d#(a(x1)) 187.92/47.88 b#(c(a(x1))) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(a(x1)) 187.92/47.88 b#(c(a(x1))) -> a#(b(c(x1))) -> a#(a(x1)) -> a#(b(a(x1))) 187.92/47.88 b#(c(a(x1))) -> c#(x1) -> c#(a(x1)) -> c#(x1) 187.92/47.88 b#(c(a(x1))) -> c#(x1) -> c#(a(x1)) -> a#(c(x1)) 187.92/47.88 b#(c(a(x1))) -> c#(x1) -> c#(b(x1)) -> d#(x1) 187.92/47.88 b#(c(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> c#(x1) 187.92/47.88 b#(c(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> b#(c(x1)) 187.92/47.88 b#(c(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> a#(b(c(x1))) 187.92/47.88 b#(c(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> c#(x1) 187.92/47.88 b#(c(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> b#(c(x1)) 187.92/47.88 b#(c(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> a#(b(c(x1))) 187.92/47.88 b#(a(a(x1))) -> a#(b(c(x1))) -> a#(d(x1)) -> a#(x1) 187.92/47.88 b#(a(a(x1))) -> a#(b(c(x1))) -> a#(d(x1)) -> d#(a(x1)) 187.92/47.88 b#(a(a(x1))) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(a(x1)) 187.92/47.88 b#(a(a(x1))) -> a#(b(c(x1))) -> a#(a(x1)) -> a#(b(a(x1))) 187.92/47.88 b#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> c#(x1) 187.92/47.88 b#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> a#(c(x1)) 187.92/47.88 b#(a(a(x1))) -> c#(x1) -> c#(b(x1)) -> d#(x1) 187.92/47.88 b#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> c#(x1) 187.92/47.88 b#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> b#(c(x1)) 187.92/47.88 b#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> a#(b(c(x1))) 187.92/47.89 b#(a(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> c#(x1) 187.92/47.89 b#(a(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> b#(c(x1)) 187.92/47.89 b#(a(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> a#(b(c(x1))) 187.92/47.89 Arctic Interpretation Processor: 187.92/47.89 dimension: 1 187.92/47.89 usable rules: 187.92/47.89 b(a(a(x1))) -> a(b(c(x1))) 187.92/47.89 c(a(x1)) -> a(c(x1)) 187.92/47.89 b(c(a(x1))) -> a(b(c(x1))) 187.92/47.89 c(b(x1)) -> d(x1) 187.92/47.89 d(x1) -> b(a(x1)) 187.92/47.89 a(d(x1)) -> d(a(x1)) 187.92/47.89 a(a(x1)) -> a(b(a(x1))) 187.92/47.89 interpretation: 187.92/47.89 [d#](x0) = 1x0, 187.92/47.89 187.92/47.89 [a#](x0) = 1x0, 187.92/47.89 187.92/47.89 [c#](x0) = 2x0, 187.92/47.89 187.92/47.89 [b#](x0) = x0, 187.92/47.89 187.92/47.89 [d](x0) = 1x0, 187.92/47.89 187.92/47.89 [c](x0) = 1x0, 187.92/47.89 187.92/47.89 [b](x0) = x0, 187.92/47.89 187.92/47.89 [a](x0) = 1x0 187.92/47.89 orientation: 187.92/47.89 b#(a(a(x1))) = 2x1 >= 2x1 = c#(x1) 187.92/47.89 187.92/47.89 b#(a(a(x1))) = 2x1 >= 1x1 = b#(c(x1)) 187.92/47.89 187.92/47.89 b#(a(a(x1))) = 2x1 >= 2x1 = a#(b(c(x1))) 187.92/47.89 187.92/47.89 c#(a(x1)) = 3x1 >= 2x1 = c#(x1) 187.92/47.89 187.92/47.89 c#(a(x1)) = 3x1 >= 2x1 = a#(c(x1)) 187.92/47.89 187.92/47.89 b#(c(a(x1))) = 2x1 >= 2x1 = c#(x1) 187.92/47.89 187.92/47.89 b#(c(a(x1))) = 2x1 >= 1x1 = b#(c(x1)) 187.92/47.89 187.92/47.89 b#(c(a(x1))) = 2x1 >= 2x1 = a#(b(c(x1))) 187.92/47.89 187.92/47.89 c#(b(x1)) = 2x1 >= 1x1 = d#(x1) 187.92/47.89 187.92/47.89 d#(x1) = 1x1 >= 1x1 = a#(x1) 187.92/47.89 187.92/47.89 d#(x1) = 1x1 >= 1x1 = b#(a(x1)) 187.92/47.89 187.92/47.89 a#(d(x1)) = 2x1 >= 1x1 = a#(x1) 187.92/47.89 187.92/47.89 a#(d(x1)) = 2x1 >= 2x1 = d#(a(x1)) 187.92/47.89 187.92/47.89 a#(a(x1)) = 2x1 >= 1x1 = b#(a(x1)) 187.92/47.89 187.92/47.89 a#(a(x1)) = 2x1 >= 2x1 = a#(b(a(x1))) 187.92/47.89 187.92/47.89 b(a(a(x1))) = 2x1 >= 2x1 = a(b(c(x1))) 187.92/47.89 187.92/47.89 c(a(x1)) = 2x1 >= 2x1 = a(c(x1)) 187.92/47.89 187.92/47.89 b(c(a(x1))) = 2x1 >= 2x1 = a(b(c(x1))) 187.92/47.89 187.92/47.89 c(b(x1)) = 1x1 >= 1x1 = d(x1) 187.92/47.89 187.92/47.89 d(x1) = 1x1 >= 1x1 = b(a(x1)) 187.92/47.89 187.92/47.89 a(d(x1)) = 2x1 >= 2x1 = d(a(x1)) 187.92/47.89 187.92/47.89 a(a(x1)) = 2x1 >= 2x1 = a(b(a(x1))) 187.92/47.89 problem: 187.92/47.89 DPs: 187.92/47.89 b#(a(a(x1))) -> c#(x1) 187.92/47.89 b#(a(a(x1))) -> a#(b(c(x1))) 187.92/47.89 b#(c(a(x1))) -> c#(x1) 187.92/47.89 b#(c(a(x1))) -> a#(b(c(x1))) 187.92/47.89 d#(x1) -> a#(x1) 187.92/47.89 d#(x1) -> b#(a(x1)) 187.92/47.89 a#(d(x1)) -> d#(a(x1)) 187.92/47.89 a#(a(x1)) -> a#(b(a(x1))) 187.92/47.89 TRS: 187.92/47.89 b(a(a(x1))) -> a(b(c(x1))) 187.92/47.89 c(a(x1)) -> a(c(x1)) 187.92/47.89 b(c(a(x1))) -> a(b(c(x1))) 187.92/47.89 c(b(x1)) -> d(x1) 187.92/47.89 d(x1) -> b(a(x1)) 187.92/47.89 a(d(x1)) -> d(a(x1)) 187.92/47.89 a(a(x1)) -> a(b(a(x1))) 187.92/47.89 Restore Modifier: 187.92/47.89 DPs: 187.92/47.89 b#(a(a(x1))) -> c#(x1) 187.92/47.89 b#(a(a(x1))) -> a#(b(c(x1))) 187.92/47.89 b#(c(a(x1))) -> c#(x1) 187.92/47.89 b#(c(a(x1))) -> a#(b(c(x1))) 187.92/47.89 d#(x1) -> a#(x1) 187.92/47.89 d#(x1) -> b#(a(x1)) 187.92/47.89 a#(d(x1)) -> d#(a(x1)) 187.92/47.89 a#(a(x1)) -> a#(b(a(x1))) 187.92/47.89 TRS: 187.92/47.89 b(a(a(x1))) -> a(b(c(x1))) 187.92/47.89 c(a(x1)) -> a(c(x1)) 187.92/47.89 b(c(a(x1))) -> a(b(c(x1))) 187.92/47.89 c(b(x1)) -> d(x1) 187.92/47.89 d(x1) -> b(a(x1)) 187.92/47.89 a(d(x1)) -> d(a(x1)) 187.92/47.89 a(a(x1)) -> a(b(a(x1))) 187.92/47.89 EDG Processor: 187.92/47.89 DPs: 187.92/47.89 b#(a(a(x1))) -> c#(x1) 187.92/47.89 b#(a(a(x1))) -> a#(b(c(x1))) 187.92/47.89 b#(c(a(x1))) -> c#(x1) 187.92/47.89 b#(c(a(x1))) -> a#(b(c(x1))) 187.92/47.89 d#(x1) -> a#(x1) 187.92/47.89 d#(x1) -> b#(a(x1)) 187.92/47.89 a#(d(x1)) -> d#(a(x1)) 187.92/47.89 a#(a(x1)) -> a#(b(a(x1))) 187.92/47.89 TRS: 187.92/47.89 b(a(a(x1))) -> a(b(c(x1))) 187.92/47.89 c(a(x1)) -> a(c(x1)) 187.92/47.89 b(c(a(x1))) -> a(b(c(x1))) 187.92/47.89 c(b(x1)) -> d(x1) 187.92/47.89 d(x1) -> b(a(x1)) 187.92/47.89 a(d(x1)) -> d(a(x1)) 187.92/47.89 a(a(x1)) -> a(b(a(x1))) 187.92/47.89 graph: 187.92/47.89 d#(x1) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1))) 187.92/47.89 d#(x1) -> a#(x1) -> a#(d(x1)) -> d#(a(x1)) 187.92/47.89 d#(x1) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(c(x1))) 187.92/47.89 d#(x1) -> b#(a(x1)) -> b#(a(a(x1))) -> c#(x1) 187.92/47.89 a#(d(x1)) -> d#(a(x1)) -> d#(x1) -> b#(a(x1)) 187.92/47.89 a#(d(x1)) -> d#(a(x1)) -> d#(x1) -> a#(x1) 187.92/47.89 a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(x1))) 187.92/47.89 a#(a(x1)) -> a#(b(a(x1))) -> a#(d(x1)) -> d#(a(x1)) 187.92/47.89 b#(c(a(x1))) -> a#(b(c(x1))) -> a#(a(x1)) -> a#(b(a(x1))) 187.92/47.89 b#(c(a(x1))) -> a#(b(c(x1))) -> a#(d(x1)) -> d#(a(x1)) 187.92/47.89 b#(a(a(x1))) -> a#(b(c(x1))) -> a#(a(x1)) -> a#(b(a(x1))) 187.92/47.89 b#(a(a(x1))) -> a#(b(c(x1))) -> a#(d(x1)) -> d#(a(x1)) 187.92/47.89 SCC Processor: 187.92/47.89 #sccs: 1 187.92/47.89 #rules: 5 187.92/47.89 #arcs: 12/64 187.92/47.89 DPs: 187.92/47.89 d#(x1) -> a#(x1) 187.92/47.90 a#(d(x1)) -> d#(a(x1)) 187.92/47.90 d#(x1) -> b#(a(x1)) 187.92/47.90 b#(a(a(x1))) -> a#(b(c(x1))) 187.92/47.90 a#(a(x1)) -> a#(b(a(x1))) 187.92/47.90 TRS: 187.92/47.90 b(a(a(x1))) -> a(b(c(x1))) 187.92/47.90 c(a(x1)) -> a(c(x1)) 187.92/47.90 b(c(a(x1))) -> a(b(c(x1))) 187.92/47.90 c(b(x1)) -> d(x1) 187.92/47.90 d(x1) -> b(a(x1)) 187.92/47.90 a(d(x1)) -> d(a(x1)) 187.92/47.90 a(a(x1)) -> a(b(a(x1))) 187.92/47.90 Arctic Interpretation Processor: 187.92/47.90 dimension: 1 187.92/47.90 usable rules: 187.92/47.90 b(a(a(x1))) -> a(b(c(x1))) 187.92/47.90 b(c(a(x1))) -> a(b(c(x1))) 187.92/47.90 d(x1) -> b(a(x1)) 187.92/47.90 a(d(x1)) -> d(a(x1)) 187.92/47.90 a(a(x1)) -> a(b(a(x1))) 187.92/47.90 interpretation: 187.92/47.90 [d#](x0) = 8x0 + 1, 187.92/47.90 187.92/47.90 [a#](x0) = x0 + 0, 187.92/47.90 187.92/47.90 [b#](x0) = x0 + 0, 187.92/47.90 187.92/47.90 [d](x0) = 8x0 + 8, 187.92/47.90 187.92/47.90 [c](x0) = 10, 187.92/47.90 187.92/47.90 [b](x0) = 0, 187.92/47.90 187.92/47.90 [a](x0) = x0 + 0 187.92/47.90 orientation: 187.92/47.90 d#(x1) = 8x1 + 1 >= x1 + 0 = a#(x1) 187.92/47.90 187.92/47.90 a#(d(x1)) = 8x1 + 8 >= 8x1 + 8 = d#(a(x1)) 187.92/47.90 187.92/47.90 d#(x1) = 8x1 + 1 >= x1 + 0 = b#(a(x1)) 187.92/47.90 187.92/47.90 b#(a(a(x1))) = x1 + 0 >= 0 = a#(b(c(x1))) 187.92/47.90 187.92/47.90 a#(a(x1)) = x1 + 0 >= 0 = a#(b(a(x1))) 187.92/47.90 187.92/47.90 b(a(a(x1))) = 0 >= 0 = a(b(c(x1))) 187.92/47.90 187.92/47.90 c(a(x1)) = 10 >= 10 = a(c(x1)) 187.92/47.90 187.92/47.90 b(c(a(x1))) = 0 >= 0 = a(b(c(x1))) 187.92/47.90 187.92/47.90 c(b(x1)) = 10 >= 8x1 + 8 = d(x1) 187.92/47.90 187.92/47.90 d(x1) = 8x1 + 8 >= 0 = b(a(x1)) 187.92/47.90 187.92/47.90 a(d(x1)) = 8x1 + 8 >= 8x1 + 8 = d(a(x1)) 187.92/47.90 187.92/47.90 a(a(x1)) = x1 + 0 >= 0 = a(b(a(x1))) 187.92/47.90 problem: 187.92/47.90 DPs: 187.92/47.90 a#(d(x1)) -> d#(a(x1)) 187.92/47.90 b#(a(a(x1))) -> a#(b(c(x1))) 187.92/47.90 a#(a(x1)) -> a#(b(a(x1))) 187.92/47.90 TRS: 187.92/47.90 b(a(a(x1))) -> a(b(c(x1))) 187.92/47.90 c(a(x1)) -> a(c(x1)) 187.92/47.90 b(c(a(x1))) -> a(b(c(x1))) 187.92/47.90 c(b(x1)) -> d(x1) 187.92/47.90 d(x1) -> b(a(x1)) 187.92/47.90 a(d(x1)) -> d(a(x1)) 187.92/47.90 a(a(x1)) -> a(b(a(x1))) 187.92/47.90 Restore Modifier: 187.92/47.90 DPs: 187.92/47.90 a#(d(x1)) -> d#(a(x1)) 187.92/47.90 b#(a(a(x1))) -> a#(b(c(x1))) 187.92/47.90 a#(a(x1)) -> a#(b(a(x1))) 187.92/47.90 TRS: 187.92/47.90 b(a(a(x1))) -> a(b(c(x1))) 187.92/47.90 c(a(x1)) -> a(c(x1)) 187.92/47.90 b(c(a(x1))) -> a(b(c(x1))) 187.92/47.90 c(b(x1)) -> d(x1) 187.92/47.90 d(x1) -> b(a(x1)) 187.92/47.90 a(d(x1)) -> d(a(x1)) 187.92/47.90 a(a(x1)) -> a(b(a(x1))) 187.92/47.90 EDG Processor: 187.92/47.90 DPs: 187.92/47.90 a#(d(x1)) -> d#(a(x1)) 187.92/47.90 b#(a(a(x1))) -> a#(b(c(x1))) 187.92/47.90 a#(a(x1)) -> a#(b(a(x1))) 187.92/47.90 TRS: 187.92/47.90 b(a(a(x1))) -> a(b(c(x1))) 187.92/47.90 c(a(x1)) -> a(c(x1)) 187.92/47.90 b(c(a(x1))) -> a(b(c(x1))) 187.92/47.90 c(b(x1)) -> d(x1) 187.92/47.90 d(x1) -> b(a(x1)) 187.92/47.90 a(d(x1)) -> d(a(x1)) 187.92/47.90 a(a(x1)) -> a(b(a(x1))) 187.92/47.90 graph: 187.92/47.90 a#(a(x1)) -> a#(b(a(x1))) -> a#(d(x1)) -> d#(a(x1)) 187.92/47.90 a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(x1))) 187.92/47.90 b#(a(a(x1))) -> a#(b(c(x1))) -> a#(d(x1)) -> d#(a(x1)) 187.92/47.90 b#(a(a(x1))) -> a#(b(c(x1))) -> a#(a(x1)) -> a#(b(a(x1))) 187.92/47.90 SCC Processor: 187.92/47.90 #sccs: 1 187.92/47.90 #rules: 1 187.92/47.90 #arcs: 4/9 187.92/47.90 DPs: 187.92/47.90 a#(a(x1)) -> a#(b(a(x1))) 187.92/47.90 TRS: 187.92/47.90 b(a(a(x1))) -> a(b(c(x1))) 187.92/47.90 c(a(x1)) -> a(c(x1)) 187.92/47.90 b(c(a(x1))) -> a(b(c(x1))) 187.92/47.90 c(b(x1)) -> d(x1) 187.92/47.90 d(x1) -> b(a(x1)) 187.92/47.90 a(d(x1)) -> d(a(x1)) 187.92/47.90 a(a(x1)) -> a(b(a(x1))) 187.92/47.90 Arctic Interpretation Processor: 187.92/47.90 dimension: 1 187.92/47.90 usable rules: 187.92/47.90 b(a(a(x1))) -> a(b(c(x1))) 187.92/47.90 c(a(x1)) -> a(c(x1)) 187.92/47.90 b(c(a(x1))) -> a(b(c(x1))) 187.92/47.90 c(b(x1)) -> d(x1) 187.92/47.90 d(x1) -> b(a(x1)) 187.92/47.90 a(d(x1)) -> d(a(x1)) 187.92/47.90 a(a(x1)) -> a(b(a(x1))) 187.92/47.90 interpretation: 187.92/47.90 [a#](x0) = 1x0 + 8, 187.92/47.90 187.92/47.90 [d](x0) = 8x0 + 11, 187.92/47.90 187.92/47.90 [c](x0) = 15x0, 187.92/47.90 187.92/47.90 [b](x0) = -7x0 + 1, 187.92/47.90 187.92/47.90 [a](x0) = 15x0 + 8 187.92/47.90 orientation: 187.92/47.90 a#(a(x1)) = 16x1 + 9 >= 9x1 + 8 = a#(b(a(x1))) 187.92/47.90 187.92/47.90 b(a(a(x1))) = 23x1 + 16 >= 23x1 + 16 = a(b(c(x1))) 187.92/47.90 187.92/47.90 c(a(x1)) = 30x1 + 23 >= 30x1 + 8 = a(c(x1)) 187.92/47.90 187.92/47.90 b(c(a(x1))) = 23x1 + 16 >= 23x1 + 16 = a(b(c(x1))) 187.92/47.90 187.92/47.90 c(b(x1)) = 8x1 + 16 >= 8x1 + 11 = d(x1) 187.92/47.90 187.92/47.90 d(x1) = 8x1 + 11 >= 8x1 + 1 = b(a(x1)) 187.92/47.90 187.92/47.90 a(d(x1)) = 23x1 + 26 >= 23x1 + 16 = d(a(x1)) 187.92/47.90 187.92/47.90 a(a(x1)) = 30x1 + 23 >= 23x1 + 16 = a(b(a(x1))) 187.92/47.90 problem: 187.92/47.90 DPs: 187.92/47.90 187.92/47.90 TRS: 187.92/47.90 b(a(a(x1))) -> a(b(c(x1))) 187.92/47.90 c(a(x1)) -> a(c(x1)) 187.92/47.90 b(c(a(x1))) -> a(b(c(x1))) 187.92/47.90 c(b(x1)) -> d(x1) 187.92/47.90 d(x1) -> b(a(x1)) 187.92/47.90 a(d(x1)) -> d(a(x1)) 187.92/47.90 a(a(x1)) -> a(b(a(x1))) 187.92/47.90 Qed 187.92/47.90 EOF