177.32/44.94 YES 177.32/44.95 177.32/44.95 Problem: 177.32/44.95 a(a(x1)) -> a(b(b(c(x1)))) 177.32/44.95 c(a(x1)) -> x1 177.32/44.95 c(b(x1)) -> a(c(x1)) 177.32/44.95 177.32/44.95 Proof: 177.32/44.95 DP Processor: 177.32/44.95 DPs: 177.32/44.95 a#(a(x1)) -> c#(x1) 177.32/44.95 a#(a(x1)) -> a#(b(b(c(x1)))) 177.32/44.95 c#(b(x1)) -> c#(x1) 177.32/44.95 c#(b(x1)) -> a#(c(x1)) 177.32/44.95 TRS: 177.32/44.95 a(a(x1)) -> a(b(b(c(x1)))) 177.32/44.95 c(a(x1)) -> x1 177.32/44.95 c(b(x1)) -> a(c(x1)) 177.32/44.95 TDG Processor: 177.32/44.95 DPs: 177.32/44.95 a#(a(x1)) -> c#(x1) 177.32/44.95 a#(a(x1)) -> a#(b(b(c(x1)))) 177.32/44.95 c#(b(x1)) -> c#(x1) 177.32/44.95 c#(b(x1)) -> a#(c(x1)) 177.32/44.95 TRS: 177.32/44.95 a(a(x1)) -> a(b(b(c(x1)))) 177.32/44.95 c(a(x1)) -> x1 177.32/44.95 c(b(x1)) -> a(c(x1)) 177.32/44.95 graph: 177.32/44.95 c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1)) 177.32/44.95 c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1) 177.32/44.95 c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(b(c(x1)))) 177.32/44.95 c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(x1) 177.32/44.95 a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1)) 177.32/44.95 a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1) 177.32/44.95 a#(a(x1)) -> a#(b(b(c(x1)))) -> a#(a(x1)) -> a#(b(b(c(x1)))) 177.32/44.95 a#(a(x1)) -> a#(b(b(c(x1)))) -> a#(a(x1)) -> c#(x1) 177.32/44.95 EDG Processor: 177.32/44.95 DPs: 177.32/44.95 a#(a(x1)) -> c#(x1) 177.32/44.95 a#(a(x1)) -> a#(b(b(c(x1)))) 177.32/44.95 c#(b(x1)) -> c#(x1) 177.32/44.95 c#(b(x1)) -> a#(c(x1)) 177.32/44.95 TRS: 177.32/44.95 a(a(x1)) -> a(b(b(c(x1)))) 177.32/44.95 c(a(x1)) -> x1 177.32/44.95 c(b(x1)) -> a(c(x1)) 177.32/44.95 graph: 177.32/44.95 c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1) 177.32/44.95 c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1)) 177.32/44.95 c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(x1) 177.32/44.95 c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(b(c(x1)))) 177.32/44.95 a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1) 177.32/44.95 a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1)) 177.32/44.95 SCC Processor: 177.32/44.95 #sccs: 1 177.32/44.95 #rules: 3 177.32/44.95 #arcs: 6/16 177.32/44.95 DPs: 177.32/44.95 c#(b(x1)) -> c#(x1) 177.32/44.95 c#(b(x1)) -> a#(c(x1)) 177.32/44.95 a#(a(x1)) -> c#(x1) 177.32/44.95 TRS: 177.32/44.95 a(a(x1)) -> a(b(b(c(x1)))) 177.32/44.95 c(a(x1)) -> x1 177.32/44.95 c(b(x1)) -> a(c(x1)) 177.32/44.95 Arctic Interpretation Processor: 177.32/44.95 dimension: 2 177.32/44.95 usable rules: 177.32/44.95 a(a(x1)) -> a(b(b(c(x1)))) 177.32/44.95 c(a(x1)) -> x1 177.32/44.95 c(b(x1)) -> a(c(x1)) 177.32/44.95 interpretation: 177.32/44.95 [c#](x0) = [0 1]x0 + [2], 177.32/44.95 177.32/44.95 [a#](x0) = [0 0]x0 + [0], 177.32/44.95 177.32/44.95 [1 0] [2] 177.32/44.95 [b](x0) = [0 0]x0 + [2], 177.32/44.95 177.32/44.95 [-& 0 ] [0] 177.32/44.95 [c](x0) = [0 -&]x0 + [0], 177.32/44.95 177.32/44.95 [-& 0 ] [0] 177.32/44.95 [a](x0) = [0 1 ]x0 + [2] 177.32/44.95 orientation: 177.32/44.95 c#(b(x1)) = [1 1]x1 + [3] >= [0 1]x1 + [2] = c#(x1) 177.32/44.95 177.32/44.95 c#(b(x1)) = [1 1]x1 + [3] >= [0 0]x1 + [0] = a#(c(x1)) 177.32/44.95 177.32/44.95 a#(a(x1)) = [0 1]x1 + [2] >= [0 1]x1 + [2] = c#(x1) 177.32/44.95 177.32/44.95 [0 1] [2] [0 1] [2] 177.32/44.95 a(a(x1)) = [1 2]x1 + [3] >= [1 2]x1 + [3] = a(b(b(c(x1)))) 177.32/44.95 177.32/44.95 [0 1 ] [2] 177.32/44.95 c(a(x1)) = [-& 0 ]x1 + [0] >= x1 = x1 177.32/44.95 177.32/44.95 [0 0] [2] [0 -&] [0] 177.32/44.95 c(b(x1)) = [1 0]x1 + [2] >= [1 0 ]x1 + [2] = a(c(x1)) 177.32/44.95 problem: 177.32/44.95 DPs: 177.32/44.95 c#(b(x1)) -> c#(x1) 177.32/44.95 a#(a(x1)) -> c#(x1) 177.32/44.95 TRS: 177.32/44.95 a(a(x1)) -> a(b(b(c(x1)))) 177.32/44.95 c(a(x1)) -> x1 177.32/44.95 c(b(x1)) -> a(c(x1)) 177.32/44.95 Restore Modifier: 177.32/44.95 DPs: 177.32/44.95 c#(b(x1)) -> c#(x1) 177.32/44.95 a#(a(x1)) -> c#(x1) 177.32/44.95 TRS: 177.32/44.95 a(a(x1)) -> a(b(b(c(x1)))) 177.32/44.95 c(a(x1)) -> x1 177.32/44.95 c(b(x1)) -> a(c(x1)) 177.32/44.95 EDG Processor: 177.32/44.95 DPs: 177.32/44.95 c#(b(x1)) -> c#(x1) 177.32/44.95 a#(a(x1)) -> c#(x1) 177.32/44.95 TRS: 177.32/44.95 a(a(x1)) -> a(b(b(c(x1)))) 177.32/44.95 c(a(x1)) -> x1 177.32/44.95 c(b(x1)) -> a(c(x1)) 177.32/44.95 graph: 177.32/44.95 c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1) 177.32/44.95 a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1) 177.32/44.95 SCC Processor: 177.32/44.95 #sccs: 1 177.32/44.95 #rules: 1 177.32/44.95 #arcs: 2/4 177.32/44.95 DPs: 177.32/44.95 c#(b(x1)) -> c#(x1) 177.32/44.95 TRS: 177.32/44.95 a(a(x1)) -> a(b(b(c(x1)))) 177.32/44.95 c(a(x1)) -> x1 177.32/44.95 c(b(x1)) -> a(c(x1)) 177.32/44.95 Usable Rule Processor: 177.32/44.95 DPs: 177.32/44.95 c#(b(x1)) -> c#(x1) 177.32/44.95 TRS: 177.32/44.95 177.32/44.95 Arctic Interpretation Processor: 177.32/44.95 dimension: 4 177.32/44.95 usable rules: 177.32/44.95 177.32/44.95 interpretation: 177.32/44.95 [c#](x0) = [0 -& -& -&]x0, 177.32/44.95 177.32/44.95 [1 0 0 0] [0] 177.32/44.95 [0 0 0 0] [0] 177.32/44.95 [b](x0) = [1 0 0 0]x0 + [0] 177.32/44.95 [0 0 0 0] [0] 177.32/44.95 orientation: 177.32/44.95 c#(b(x1)) = [1 0 0 0]x1 + [0] >= [0 -& -& -&]x1 = c#(x1) 177.32/44.95 problem: 177.32/44.95 DPs: 177.32/44.95 177.32/44.95 TRS: 177.32/44.95 177.32/44.95 Qed 177.32/44.95 EOF