172.72/44.21 YES 172.72/44.22 172.72/44.22 Problem: 172.72/44.22 a(a(x1)) -> b(b(b(x1))) 172.72/44.22 a(x1) -> c(d(x1)) 172.72/44.22 b(b(x1)) -> c(c(c(x1))) 172.72/44.22 c(c(x1)) -> d(d(d(x1))) 172.72/44.22 e(d(x1)) -> a(b(c(d(e(x1))))) 172.72/44.22 b(x1) -> d(d(x1)) 172.72/44.22 e(c(x1)) -> b(a(a(e(x1)))) 172.72/44.22 c(d(d(x1))) -> a(x1) 172.72/44.22 172.72/44.22 Proof: 172.72/44.22 DP Processor: 172.72/44.22 DPs: 172.72/44.22 a#(a(x1)) -> b#(x1) 172.72/44.22 a#(a(x1)) -> b#(b(x1)) 172.72/44.22 a#(a(x1)) -> b#(b(b(x1))) 172.72/44.22 a#(x1) -> c#(d(x1)) 172.72/44.22 b#(b(x1)) -> c#(x1) 172.72/44.22 b#(b(x1)) -> c#(c(x1)) 172.72/44.22 b#(b(x1)) -> c#(c(c(x1))) 172.72/44.22 e#(d(x1)) -> e#(x1) 172.72/44.22 e#(d(x1)) -> c#(d(e(x1))) 172.72/44.22 e#(d(x1)) -> b#(c(d(e(x1)))) 172.72/44.22 e#(d(x1)) -> a#(b(c(d(e(x1))))) 172.72/44.22 e#(c(x1)) -> e#(x1) 172.72/44.22 e#(c(x1)) -> a#(e(x1)) 172.72/44.22 e#(c(x1)) -> a#(a(e(x1))) 172.72/44.22 e#(c(x1)) -> b#(a(a(e(x1)))) 172.72/44.22 c#(d(d(x1))) -> a#(x1) 172.72/44.22 TRS: 172.72/44.22 a(a(x1)) -> b(b(b(x1))) 172.72/44.22 a(x1) -> c(d(x1)) 172.72/44.22 b(b(x1)) -> c(c(c(x1))) 172.72/44.22 c(c(x1)) -> d(d(d(x1))) 172.72/44.22 e(d(x1)) -> a(b(c(d(e(x1))))) 172.72/44.22 b(x1) -> d(d(x1)) 172.72/44.22 e(c(x1)) -> b(a(a(e(x1)))) 172.72/44.22 c(d(d(x1))) -> a(x1) 172.72/44.22 TDG Processor: 172.72/44.22 DPs: 172.72/44.22 a#(a(x1)) -> b#(x1) 172.72/44.22 a#(a(x1)) -> b#(b(x1)) 172.72/44.22 a#(a(x1)) -> b#(b(b(x1))) 172.72/44.22 a#(x1) -> c#(d(x1)) 172.72/44.22 b#(b(x1)) -> c#(x1) 172.72/44.22 b#(b(x1)) -> c#(c(x1)) 172.72/44.22 b#(b(x1)) -> c#(c(c(x1))) 172.72/44.22 e#(d(x1)) -> e#(x1) 172.72/44.22 e#(d(x1)) -> c#(d(e(x1))) 172.72/44.22 e#(d(x1)) -> b#(c(d(e(x1)))) 172.72/44.22 e#(d(x1)) -> a#(b(c(d(e(x1))))) 172.72/44.22 e#(c(x1)) -> e#(x1) 172.72/44.22 e#(c(x1)) -> a#(e(x1)) 172.72/44.22 e#(c(x1)) -> a#(a(e(x1))) 172.72/44.22 e#(c(x1)) -> b#(a(a(e(x1)))) 172.72/44.22 c#(d(d(x1))) -> a#(x1) 172.72/44.22 TRS: 172.72/44.22 a(a(x1)) -> b(b(b(x1))) 172.72/44.22 a(x1) -> c(d(x1)) 172.72/44.22 b(b(x1)) -> c(c(c(x1))) 172.72/44.22 c(c(x1)) -> d(d(d(x1))) 172.72/44.22 e(d(x1)) -> a(b(c(d(e(x1))))) 172.72/44.22 b(x1) -> d(d(x1)) 172.72/44.22 e(c(x1)) -> b(a(a(e(x1)))) 172.72/44.22 c(d(d(x1))) -> a(x1) 172.72/44.22 graph: 172.72/44.22 e#(c(x1)) -> e#(x1) -> e#(c(x1)) -> b#(a(a(e(x1)))) 172.72/44.22 e#(c(x1)) -> e#(x1) -> e#(c(x1)) -> a#(a(e(x1))) 172.72/44.22 e#(c(x1)) -> e#(x1) -> e#(c(x1)) -> a#(e(x1)) 172.72/44.22 e#(c(x1)) -> e#(x1) -> e#(c(x1)) -> e#(x1) 172.72/44.22 e#(c(x1)) -> e#(x1) -> e#(d(x1)) -> a#(b(c(d(e(x1))))) 172.72/44.22 e#(c(x1)) -> e#(x1) -> e#(d(x1)) -> b#(c(d(e(x1)))) 172.72/44.22 e#(c(x1)) -> e#(x1) -> e#(d(x1)) -> c#(d(e(x1))) 172.72/44.22 e#(c(x1)) -> e#(x1) -> e#(d(x1)) -> e#(x1) 172.72/44.22 e#(c(x1)) -> b#(a(a(e(x1)))) -> b#(b(x1)) -> c#(c(c(x1))) 172.72/44.23 e#(c(x1)) -> b#(a(a(e(x1)))) -> b#(b(x1)) -> c#(c(x1)) 172.72/44.23 e#(c(x1)) -> b#(a(a(e(x1)))) -> b#(b(x1)) -> c#(x1) 172.72/44.23 e#(c(x1)) -> a#(e(x1)) -> a#(x1) -> c#(d(x1)) 172.72/44.23 e#(c(x1)) -> a#(e(x1)) -> a#(a(x1)) -> b#(b(b(x1))) 172.72/44.23 e#(c(x1)) -> a#(e(x1)) -> a#(a(x1)) -> b#(b(x1)) 172.72/44.23 e#(c(x1)) -> a#(e(x1)) -> a#(a(x1)) -> b#(x1) 172.72/44.23 e#(c(x1)) -> a#(a(e(x1))) -> a#(x1) -> c#(d(x1)) 172.72/44.23 e#(c(x1)) -> a#(a(e(x1))) -> a#(a(x1)) -> b#(b(b(x1))) 172.72/44.23 e#(c(x1)) -> a#(a(e(x1))) -> a#(a(x1)) -> b#(b(x1)) 172.72/44.23 e#(c(x1)) -> a#(a(e(x1))) -> a#(a(x1)) -> b#(x1) 172.72/44.23 e#(d(x1)) -> e#(x1) -> e#(c(x1)) -> b#(a(a(e(x1)))) 172.72/44.23 e#(d(x1)) -> e#(x1) -> e#(c(x1)) -> a#(a(e(x1))) 172.72/44.23 e#(d(x1)) -> e#(x1) -> e#(c(x1)) -> a#(e(x1)) 172.72/44.23 e#(d(x1)) -> e#(x1) -> e#(c(x1)) -> e#(x1) 172.72/44.23 e#(d(x1)) -> e#(x1) -> e#(d(x1)) -> a#(b(c(d(e(x1))))) 172.72/44.23 e#(d(x1)) -> e#(x1) -> e#(d(x1)) -> b#(c(d(e(x1)))) 172.72/44.23 e#(d(x1)) -> e#(x1) -> e#(d(x1)) -> c#(d(e(x1))) 172.72/44.23 e#(d(x1)) -> e#(x1) -> e#(d(x1)) -> e#(x1) 172.72/44.23 e#(d(x1)) -> c#(d(e(x1))) -> c#(d(d(x1))) -> a#(x1) 172.72/44.23 e#(d(x1)) -> b#(c(d(e(x1)))) -> b#(b(x1)) -> c#(c(c(x1))) 172.72/44.23 e#(d(x1)) -> b#(c(d(e(x1)))) -> b#(b(x1)) -> c#(c(x1)) 172.72/44.23 e#(d(x1)) -> b#(c(d(e(x1)))) -> b#(b(x1)) -> c#(x1) 172.72/44.23 e#(d(x1)) -> a#(b(c(d(e(x1))))) -> a#(x1) -> c#(d(x1)) 172.72/44.23 e#(d(x1)) -> a#(b(c(d(e(x1))))) -> a#(a(x1)) -> b#(b(b(x1))) 172.72/44.23 e#(d(x1)) -> a#(b(c(d(e(x1))))) -> a#(a(x1)) -> b#(b(x1)) 172.72/44.23 e#(d(x1)) -> a#(b(c(d(e(x1))))) -> a#(a(x1)) -> b#(x1) 172.72/44.23 c#(d(d(x1))) -> a#(x1) -> a#(x1) -> c#(d(x1)) 172.72/44.23 c#(d(d(x1))) -> a#(x1) -> a#(a(x1)) -> b#(b(b(x1))) 172.72/44.23 c#(d(d(x1))) -> a#(x1) -> a#(a(x1)) -> b#(b(x1)) 172.72/44.23 c#(d(d(x1))) -> a#(x1) -> a#(a(x1)) -> b#(x1) 172.72/44.23 b#(b(x1)) -> c#(c(c(x1))) -> c#(d(d(x1))) -> a#(x1) 172.72/44.23 b#(b(x1)) -> c#(c(x1)) -> c#(d(d(x1))) -> a#(x1) 172.72/44.23 b#(b(x1)) -> c#(x1) -> c#(d(d(x1))) -> a#(x1) 172.72/44.23 a#(a(x1)) -> b#(b(b(x1))) -> b#(b(x1)) -> c#(c(c(x1))) 172.72/44.23 a#(a(x1)) -> b#(b(b(x1))) -> b#(b(x1)) -> c#(c(x1)) 172.72/44.23 a#(a(x1)) -> b#(b(b(x1))) -> b#(b(x1)) -> c#(x1) 172.72/44.23 a#(a(x1)) -> b#(b(x1)) -> b#(b(x1)) -> c#(c(c(x1))) 172.72/44.23 a#(a(x1)) -> b#(b(x1)) -> b#(b(x1)) -> c#(c(x1)) 172.72/44.23 a#(a(x1)) -> b#(b(x1)) -> b#(b(x1)) -> c#(x1) 172.72/44.23 a#(a(x1)) -> b#(x1) -> b#(b(x1)) -> c#(c(c(x1))) 172.72/44.23 a#(a(x1)) -> b#(x1) -> b#(b(x1)) -> c#(c(x1)) 172.72/44.23 a#(a(x1)) -> b#(x1) -> b#(b(x1)) -> c#(x1) 172.72/44.23 a#(x1) -> c#(d(x1)) -> c#(d(d(x1))) -> a#(x1) 172.72/44.23 SCC Processor: 172.72/44.23 #sccs: 2 172.72/44.23 #rules: 10 172.72/44.23 #arcs: 52/256 172.72/44.23 DPs: 172.72/44.23 e#(c(x1)) -> e#(x1) 172.72/44.23 e#(d(x1)) -> e#(x1) 172.72/44.23 TRS: 172.72/44.23 a(a(x1)) -> b(b(b(x1))) 172.72/44.23 a(x1) -> c(d(x1)) 172.72/44.23 b(b(x1)) -> c(c(c(x1))) 172.72/44.23 c(c(x1)) -> d(d(d(x1))) 172.72/44.23 e(d(x1)) -> a(b(c(d(e(x1))))) 172.72/44.23 b(x1) -> d(d(x1)) 172.72/44.23 e(c(x1)) -> b(a(a(e(x1)))) 172.72/44.23 c(d(d(x1))) -> a(x1) 172.72/44.23 Usable Rule Processor: 172.72/44.23 DPs: 172.72/44.23 e#(c(x1)) -> e#(x1) 172.72/44.23 e#(d(x1)) -> e#(x1) 172.72/44.23 TRS: 172.72/44.23 172.72/44.23 Arctic Interpretation Processor: 172.72/44.23 dimension: 1 172.72/44.23 usable rules: 172.72/44.23 172.72/44.23 interpretation: 172.72/44.23 [e#](x0) = x0, 172.72/44.23 172.72/44.23 [c](x0) = x0, 172.72/44.23 172.72/44.23 [d](x0) = 1x0 + 9 172.72/44.23 orientation: 172.72/44.23 e#(c(x1)) = x1 >= x1 = e#(x1) 172.72/44.23 172.72/44.23 e#(d(x1)) = 1x1 + 9 >= x1 = e#(x1) 172.72/44.23 problem: 172.72/44.23 DPs: 172.72/44.23 e#(c(x1)) -> e#(x1) 172.72/44.23 TRS: 172.72/44.23 172.72/44.23 Restore Modifier: 172.72/44.23 DPs: 172.72/44.23 e#(c(x1)) -> e#(x1) 172.72/44.23 TRS: 172.72/44.23 a(a(x1)) -> b(b(b(x1))) 172.72/44.23 a(x1) -> c(d(x1)) 172.72/44.23 b(b(x1)) -> c(c(c(x1))) 172.72/44.23 c(c(x1)) -> d(d(d(x1))) 172.72/44.23 e(d(x1)) -> a(b(c(d(e(x1))))) 172.72/44.23 b(x1) -> d(d(x1)) 172.72/44.23 e(c(x1)) -> b(a(a(e(x1)))) 172.72/44.23 c(d(d(x1))) -> a(x1) 172.72/44.23 EDG Processor: 172.72/44.23 DPs: 172.72/44.23 e#(c(x1)) -> e#(x1) 172.72/44.23 TRS: 172.72/44.23 a(a(x1)) -> b(b(b(x1))) 172.72/44.23 a(x1) -> c(d(x1)) 172.72/44.23 b(b(x1)) -> c(c(c(x1))) 172.72/44.23 c(c(x1)) -> d(d(d(x1))) 172.72/44.23 e(d(x1)) -> a(b(c(d(e(x1))))) 172.72/44.23 b(x1) -> d(d(x1)) 172.72/44.23 e(c(x1)) -> b(a(a(e(x1)))) 172.72/44.23 c(d(d(x1))) -> a(x1) 172.72/44.23 graph: 172.72/44.23 e#(c(x1)) -> e#(x1) -> e#(c(x1)) -> e#(x1) 172.72/44.23 Usable Rule Processor: 172.72/44.23 DPs: 172.72/44.23 e#(c(x1)) -> e#(x1) 172.72/44.23 TRS: 172.72/44.23 172.72/44.23 Arctic Interpretation Processor: 172.72/44.23 dimension: 4 172.72/44.23 usable rules: 172.72/44.23 172.72/44.23 interpretation: 172.72/44.23 [e#](x0) = [0 -& -& -&]x0, 172.72/44.23 172.72/44.23 [1 0 0 0] [0] 172.72/44.23 [0 0 0 0] [0] 172.72/44.23 [c](x0) = [1 0 0 0]x0 + [0] 172.72/44.23 [0 0 0 0] [0] 172.72/44.23 orientation: 172.72/44.23 e#(c(x1)) = [1 0 0 0]x1 + [0] >= [0 -& -& -&]x1 = e#(x1) 172.72/44.23 problem: 172.72/44.23 DPs: 172.72/44.23 172.72/44.23 TRS: 172.72/44.23 172.72/44.23 Qed 172.72/44.23 172.72/44.23 DPs: 172.72/44.23 c#(d(d(x1))) -> a#(x1) 172.72/44.23 a#(a(x1)) -> b#(x1) 172.72/44.23 b#(b(x1)) -> c#(x1) 172.72/44.23 b#(b(x1)) -> c#(c(x1)) 172.72/44.23 b#(b(x1)) -> c#(c(c(x1))) 172.72/44.23 a#(a(x1)) -> b#(b(x1)) 172.72/44.23 a#(a(x1)) -> b#(b(b(x1))) 172.72/44.23 a#(x1) -> c#(d(x1)) 172.72/44.23 TRS: 172.72/44.23 a(a(x1)) -> b(b(b(x1))) 172.72/44.23 a(x1) -> c(d(x1)) 172.72/44.23 b(b(x1)) -> c(c(c(x1))) 172.72/44.23 c(c(x1)) -> d(d(d(x1))) 172.72/44.23 e(d(x1)) -> a(b(c(d(e(x1))))) 172.72/44.23 b(x1) -> d(d(x1)) 172.72/44.23 e(c(x1)) -> b(a(a(e(x1)))) 172.72/44.23 c(d(d(x1))) -> a(x1) 172.72/44.23 Usable Rule Processor: 172.72/44.23 DPs: 172.72/44.23 c#(d(d(x1))) -> a#(x1) 172.72/44.23 a#(a(x1)) -> b#(x1) 172.72/44.23 b#(b(x1)) -> c#(x1) 172.72/44.23 b#(b(x1)) -> c#(c(x1)) 172.72/44.23 b#(b(x1)) -> c#(c(c(x1))) 172.72/44.23 a#(a(x1)) -> b#(b(x1)) 172.72/44.23 a#(a(x1)) -> b#(b(b(x1))) 172.72/44.23 a#(x1) -> c#(d(x1)) 172.72/44.23 TRS: 172.72/44.23 c(c(x1)) -> d(d(d(x1))) 172.72/44.23 c(d(d(x1))) -> a(x1) 172.72/44.23 a(a(x1)) -> b(b(b(x1))) 172.72/44.23 a(x1) -> c(d(x1)) 172.72/44.23 b(b(x1)) -> c(c(c(x1))) 172.72/44.23 b(x1) -> d(d(x1)) 172.72/44.23 Arctic Interpretation Processor: 172.72/44.23 dimension: 1 172.72/44.23 usable rules: 172.72/44.23 c(c(x1)) -> d(d(d(x1))) 172.72/44.23 c(d(d(x1))) -> a(x1) 172.72/44.23 a(a(x1)) -> b(b(b(x1))) 172.72/44.23 a(x1) -> c(d(x1)) 172.72/44.23 b(b(x1)) -> c(c(c(x1))) 172.72/44.23 b(x1) -> d(d(x1)) 172.72/44.23 interpretation: 172.72/44.23 [c#](x0) = 5x0, 172.72/44.23 172.72/44.23 [b#](x0) = 8x0, 172.72/44.23 172.72/44.23 [a#](x0) = 12x0, 172.72/44.23 172.72/44.23 [c](x0) = 6x0, 172.72/44.23 172.72/44.23 [d](x0) = 4x0, 172.72/44.23 172.72/44.23 [b](x0) = 9x0, 172.72/44.23 172.72/44.23 [a](x0) = 14x0 172.72/44.23 orientation: 172.72/44.23 c#(d(d(x1))) = 13x1 >= 12x1 = a#(x1) 172.72/44.23 172.72/44.23 a#(a(x1)) = 26x1 >= 8x1 = b#(x1) 172.72/44.23 172.72/44.23 b#(b(x1)) = 17x1 >= 5x1 = c#(x1) 172.72/44.23 172.72/44.23 b#(b(x1)) = 17x1 >= 11x1 = c#(c(x1)) 172.72/44.23 172.72/44.23 b#(b(x1)) = 17x1 >= 17x1 = c#(c(c(x1))) 172.72/44.23 172.72/44.23 a#(a(x1)) = 26x1 >= 17x1 = b#(b(x1)) 172.72/44.23 172.72/44.23 a#(a(x1)) = 26x1 >= 26x1 = b#(b(b(x1))) 172.72/44.23 172.72/44.23 a#(x1) = 12x1 >= 9x1 = c#(d(x1)) 172.72/44.23 172.72/44.23 c(c(x1)) = 12x1 >= 12x1 = d(d(d(x1))) 172.72/44.23 172.72/44.23 c(d(d(x1))) = 14x1 >= 14x1 = a(x1) 172.72/44.23 172.72/44.23 a(a(x1)) = 28x1 >= 27x1 = b(b(b(x1))) 172.72/44.23 172.72/44.23 a(x1) = 14x1 >= 10x1 = c(d(x1)) 172.72/44.23 172.72/44.23 b(b(x1)) = 18x1 >= 18x1 = c(c(c(x1))) 172.72/44.23 172.72/44.23 b(x1) = 9x1 >= 8x1 = d(d(x1)) 172.72/44.23 problem: 172.72/44.23 DPs: 172.72/44.23 b#(b(x1)) -> c#(c(c(x1))) 172.72/44.23 a#(a(x1)) -> b#(b(b(x1))) 172.72/44.23 TRS: 172.72/44.23 c(c(x1)) -> d(d(d(x1))) 172.72/44.23 c(d(d(x1))) -> a(x1) 172.72/44.23 a(a(x1)) -> b(b(b(x1))) 172.72/44.23 a(x1) -> c(d(x1)) 172.72/44.23 b(b(x1)) -> c(c(c(x1))) 172.72/44.23 b(x1) -> d(d(x1)) 172.72/44.23 Restore Modifier: 172.72/44.23 DPs: 172.72/44.23 b#(b(x1)) -> c#(c(c(x1))) 172.72/44.23 a#(a(x1)) -> b#(b(b(x1))) 172.72/44.23 TRS: 172.72/44.23 a(a(x1)) -> b(b(b(x1))) 172.72/44.23 a(x1) -> c(d(x1)) 172.72/44.23 b(b(x1)) -> c(c(c(x1))) 172.72/44.23 c(c(x1)) -> d(d(d(x1))) 172.72/44.23 e(d(x1)) -> a(b(c(d(e(x1))))) 172.72/44.23 b(x1) -> d(d(x1)) 172.72/44.23 e(c(x1)) -> b(a(a(e(x1)))) 172.72/44.23 c(d(d(x1))) -> a(x1) 172.72/44.23 EDG Processor: 172.72/44.23 DPs: 172.72/44.23 b#(b(x1)) -> c#(c(c(x1))) 172.72/44.23 a#(a(x1)) -> b#(b(b(x1))) 172.72/44.23 TRS: 172.72/44.23 a(a(x1)) -> b(b(b(x1))) 172.72/44.23 a(x1) -> c(d(x1)) 172.72/44.23 b(b(x1)) -> c(c(c(x1))) 172.72/44.23 c(c(x1)) -> d(d(d(x1))) 172.72/44.23 e(d(x1)) -> a(b(c(d(e(x1))))) 172.72/44.23 b(x1) -> d(d(x1)) 172.72/44.23 e(c(x1)) -> b(a(a(e(x1)))) 172.72/44.23 c(d(d(x1))) -> a(x1) 172.72/44.23 graph: 172.72/44.23 a#(a(x1)) -> b#(b(b(x1))) -> b#(b(x1)) -> c#(c(c(x1))) 172.72/44.23 SCC Processor: 172.72/44.23 #sccs: 0 172.72/44.23 #rules: 0 172.72/44.23 #arcs: 1/4 172.72/44.23 172.98/44.24 EOF