177.06/45.19 YES 177.06/45.20 177.06/45.20 Problem: 177.06/45.20 a(x1) -> x1 177.06/45.20 a(a(x1)) -> a(b(c(c(x1)))) 177.06/45.20 c(x1) -> b(x1) 177.06/45.20 c(b(x1)) -> a(x1) 177.06/45.20 177.06/45.20 Proof: 177.06/45.20 DP Processor: 177.06/45.20 DPs: 177.06/45.20 a#(a(x1)) -> c#(x1) 177.06/45.20 a#(a(x1)) -> c#(c(x1)) 177.06/45.20 a#(a(x1)) -> a#(b(c(c(x1)))) 177.06/45.20 c#(b(x1)) -> a#(x1) 177.06/45.20 TRS: 177.06/45.20 a(x1) -> x1 177.06/45.20 a(a(x1)) -> a(b(c(c(x1)))) 177.06/45.20 c(x1) -> b(x1) 177.06/45.20 c(b(x1)) -> a(x1) 177.06/45.20 TDG Processor: 177.06/45.20 DPs: 177.06/45.20 a#(a(x1)) -> c#(x1) 177.06/45.20 a#(a(x1)) -> c#(c(x1)) 177.06/45.20 a#(a(x1)) -> a#(b(c(c(x1)))) 177.06/45.20 c#(b(x1)) -> a#(x1) 177.06/45.20 TRS: 177.06/45.20 a(x1) -> x1 177.06/45.20 a(a(x1)) -> a(b(c(c(x1)))) 177.06/45.20 c(x1) -> b(x1) 177.06/45.20 c(b(x1)) -> a(x1) 177.06/45.20 graph: 177.06/45.20 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(c(c(x1)))) 177.06/45.20 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(c(x1)) 177.06/45.20 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(x1) 177.06/45.20 a#(a(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(x1) 177.06/45.20 a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(x1) 177.06/45.20 a#(a(x1)) -> a#(b(c(c(x1)))) -> a#(a(x1)) -> a#(b(c(c(x1)))) 177.06/45.20 a#(a(x1)) -> a#(b(c(c(x1)))) -> a#(a(x1)) -> c#(c(x1)) 177.06/45.20 a#(a(x1)) -> a#(b(c(c(x1)))) -> a#(a(x1)) -> c#(x1) 177.06/45.20 EDG Processor: 177.06/45.20 DPs: 177.06/45.20 a#(a(x1)) -> c#(x1) 177.06/45.20 a#(a(x1)) -> c#(c(x1)) 177.06/45.20 a#(a(x1)) -> a#(b(c(c(x1)))) 177.06/45.20 c#(b(x1)) -> a#(x1) 177.06/45.20 TRS: 177.06/45.20 a(x1) -> x1 177.06/45.20 a(a(x1)) -> a(b(c(c(x1)))) 177.06/45.20 c(x1) -> b(x1) 177.06/45.20 c(b(x1)) -> a(x1) 177.06/45.20 graph: 177.06/45.20 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(x1) 177.06/45.20 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(c(x1)) 177.06/45.20 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(c(c(x1)))) 177.06/45.20 a#(a(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(x1) 177.06/45.20 a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(x1) 177.06/45.20 SCC Processor: 177.06/45.20 #sccs: 1 177.06/45.20 #rules: 3 177.06/45.20 #arcs: 5/16 177.06/45.20 DPs: 177.06/45.20 c#(b(x1)) -> a#(x1) 177.06/45.20 a#(a(x1)) -> c#(c(x1)) 177.06/45.20 a#(a(x1)) -> c#(x1) 177.06/45.20 TRS: 177.06/45.20 a(x1) -> x1 177.06/45.20 a(a(x1)) -> a(b(c(c(x1)))) 177.06/45.20 c(x1) -> b(x1) 177.06/45.20 c(b(x1)) -> a(x1) 177.06/45.20 Arctic Interpretation Processor: 177.06/45.20 dimension: 2 177.06/45.20 usable rules: 177.06/45.20 a(x1) -> x1 177.06/45.20 a(a(x1)) -> a(b(c(c(x1)))) 177.06/45.20 c(x1) -> b(x1) 177.06/45.20 c(b(x1)) -> a(x1) 177.06/45.20 interpretation: 177.06/45.20 [c#](x0) = [2 3]x0 + [0], 177.06/45.20 177.06/45.20 [a#](x0) = [2 3]x0 + [0], 177.06/45.20 177.06/45.20 [0 1 ] [-&] 177.06/45.20 [b](x0) = [-& 0 ]x0 + [0 ], 177.06/45.20 177.06/45.20 [0 1] [-&] 177.06/45.20 [c](x0) = [0 0]x0 + [2 ], 177.06/45.20 177.06/45.20 [0 1] [0] 177.06/45.20 [a](x0) = [0 1]x0 + [2] 177.06/45.20 orientation: 177.06/45.20 c#(b(x1)) = [2 3]x1 + [3] >= [2 3]x1 + [0] = a#(x1) 177.06/45.20 177.06/45.20 a#(a(x1)) = [3 4]x1 + [5] >= [3 3]x1 + [5] = c#(c(x1)) 177.06/45.20 177.06/45.20 a#(a(x1)) = [3 4]x1 + [5] >= [2 3]x1 + [0] = c#(x1) 177.06/45.20 177.06/45.20 [0 1] [0] 177.06/45.20 a(x1) = [0 1]x1 + [2] >= x1 = x1 177.06/45.20 177.06/45.20 [1 2] [3] [1 2] [3] 177.06/45.20 a(a(x1)) = [1 2]x1 + [3] >= [1 2]x1 + [3] = a(b(c(c(x1)))) 177.06/45.20 177.06/45.20 [0 1] [-&] [0 1 ] [-&] 177.06/45.20 c(x1) = [0 0]x1 + [2 ] >= [-& 0 ]x1 + [0 ] = b(x1) 177.06/45.20 177.06/45.20 [0 1] [1] [0 1] [0] 177.06/45.20 c(b(x1)) = [0 1]x1 + [2] >= [0 1]x1 + [2] = a(x1) 177.06/45.20 problem: 177.06/45.20 DPs: 177.06/45.20 c#(b(x1)) -> a#(x1) 177.06/45.20 a#(a(x1)) -> c#(c(x1)) 177.06/45.20 TRS: 177.06/45.20 a(x1) -> x1 177.06/45.20 a(a(x1)) -> a(b(c(c(x1)))) 177.06/45.20 c(x1) -> b(x1) 177.06/45.20 c(b(x1)) -> a(x1) 177.06/45.20 Restore Modifier: 177.06/45.20 DPs: 177.06/45.20 c#(b(x1)) -> a#(x1) 177.06/45.20 a#(a(x1)) -> c#(c(x1)) 177.06/45.20 TRS: 177.06/45.20 a(x1) -> x1 177.06/45.20 a(a(x1)) -> a(b(c(c(x1)))) 177.06/45.20 c(x1) -> b(x1) 177.06/45.20 c(b(x1)) -> a(x1) 177.06/45.20 EDG Processor: 177.06/45.20 DPs: 177.06/45.20 c#(b(x1)) -> a#(x1) 177.06/45.20 a#(a(x1)) -> c#(c(x1)) 177.06/45.20 TRS: 177.06/45.20 a(x1) -> x1 177.06/45.20 a(a(x1)) -> a(b(c(c(x1)))) 177.06/45.20 c(x1) -> b(x1) 177.06/45.20 c(b(x1)) -> a(x1) 177.06/45.20 graph: 177.06/45.20 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(c(x1)) 177.06/45.20 a#(a(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(x1) 177.06/45.20 Arctic Interpretation Processor: 177.06/45.20 dimension: 2 177.06/45.20 usable rules: 177.06/45.20 a(x1) -> x1 177.06/45.20 a(a(x1)) -> a(b(c(c(x1)))) 177.06/45.20 c(x1) -> b(x1) 177.06/45.20 c(b(x1)) -> a(x1) 177.06/45.20 interpretation: 177.06/45.20 [c#](x0) = [0 0]x0 + [1], 177.06/45.20 177.06/45.20 [a#](x0) = [0 1]x0, 177.06/45.20 177.06/45.20 [0 1 ] [-&] 177.06/45.20 [b](x0) = [-& 0 ]x0 + [0 ], 177.06/45.20 177.06/45.20 [0 1] [0] 177.06/45.20 [c](x0) = [0 0]x0 + [3], 177.06/45.20 177.06/45.20 [0 1] [0] 177.06/45.20 [a](x0) = [0 1]x0 + [3] 177.06/45.20 orientation: 177.06/45.20 c#(b(x1)) = [0 1]x1 + [1] >= [0 1]x1 = a#(x1) 177.06/45.20 177.06/45.20 a#(a(x1)) = [1 2]x1 + [4] >= [0 1]x1 + [3] = c#(c(x1)) 177.06/45.20 177.06/45.20 [0 1] [0] 177.06/45.20 a(x1) = [0 1]x1 + [3] >= x1 = x1 177.06/45.20 177.06/45.20 [1 2] [4] [1 2] [4] 177.06/45.20 a(a(x1)) = [1 2]x1 + [4] >= [1 2]x1 + [4] = a(b(c(c(x1)))) 177.06/45.20 177.06/45.20 [0 1] [0] [0 1 ] [-&] 177.06/45.20 c(x1) = [0 0]x1 + [3] >= [-& 0 ]x1 + [0 ] = b(x1) 177.06/45.20 177.06/45.20 [0 1] [1] [0 1] [0] 177.06/45.20 c(b(x1)) = [0 1]x1 + [3] >= [0 1]x1 + [3] = a(x1) 177.06/45.20 problem: 177.06/45.20 DPs: 177.06/45.20 c#(b(x1)) -> a#(x1) 177.06/45.20 TRS: 177.06/45.20 a(x1) -> x1 177.06/45.20 a(a(x1)) -> a(b(c(c(x1)))) 177.06/45.20 c(x1) -> b(x1) 177.06/45.20 c(b(x1)) -> a(x1) 177.06/45.20 Restore Modifier: 177.06/45.20 DPs: 177.06/45.20 c#(b(x1)) -> a#(x1) 177.06/45.20 TRS: 177.06/45.20 a(x1) -> x1 177.06/45.20 a(a(x1)) -> a(b(c(c(x1)))) 177.06/45.20 c(x1) -> b(x1) 177.06/45.20 c(b(x1)) -> a(x1) 177.06/45.20 EDG Processor: 177.06/45.20 DPs: 177.06/45.20 c#(b(x1)) -> a#(x1) 177.06/45.20 TRS: 177.06/45.20 a(x1) -> x1 177.06/45.20 a(a(x1)) -> a(b(c(c(x1)))) 177.06/45.20 c(x1) -> b(x1) 177.06/45.20 c(b(x1)) -> a(x1) 177.06/45.20 graph: 177.06/45.20 177.06/45.20 SCC Processor: 177.06/45.20 #sccs: 0 177.06/45.20 #rules: 0 177.06/45.20 #arcs: 0/1 177.06/45.20 177.06/45.21 EOF