181.88/46.46 YES 182.11/46.47 182.11/46.47 Problem: 182.11/46.47 a(a(x1)) -> a(b(a(c(c(x1))))) 182.11/46.47 c(a(x1)) -> x1 182.11/46.47 c(b(x1)) -> a(x1) 182.11/46.47 182.11/46.47 Proof: 182.11/46.47 DP Processor: 182.11/46.47 DPs: 182.11/46.47 a#(a(x1)) -> c#(x1) 182.11/46.47 a#(a(x1)) -> c#(c(x1)) 182.11/46.47 a#(a(x1)) -> a#(c(c(x1))) 182.11/46.47 a#(a(x1)) -> a#(b(a(c(c(x1))))) 182.11/46.47 c#(b(x1)) -> a#(x1) 182.11/46.47 TRS: 182.11/46.47 a(a(x1)) -> a(b(a(c(c(x1))))) 182.11/46.47 c(a(x1)) -> x1 182.11/46.47 c(b(x1)) -> a(x1) 182.11/46.47 TDG Processor: 182.11/46.47 DPs: 182.11/46.47 a#(a(x1)) -> c#(x1) 182.11/46.47 a#(a(x1)) -> c#(c(x1)) 182.11/46.47 a#(a(x1)) -> a#(c(c(x1))) 182.11/46.47 a#(a(x1)) -> a#(b(a(c(c(x1))))) 182.11/46.47 c#(b(x1)) -> a#(x1) 182.11/46.47 TRS: 182.11/46.47 a(a(x1)) -> a(b(a(c(c(x1))))) 182.11/46.47 c(a(x1)) -> x1 182.11/46.47 c(b(x1)) -> a(x1) 182.11/46.47 graph: 182.11/46.47 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(a(c(c(x1))))) 182.11/46.47 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(c(c(x1))) 182.11/46.47 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(c(x1)) 182.11/46.47 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(x1) 182.11/46.47 a#(a(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(x1) 182.11/46.47 a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(x1) 182.11/46.47 a#(a(x1)) -> a#(b(a(c(c(x1))))) -> 182.11/46.47 a#(a(x1)) -> a#(b(a(c(c(x1))))) 182.11/46.47 a#(a(x1)) -> a#(b(a(c(c(x1))))) -> a#(a(x1)) -> a#(c(c(x1))) 182.11/46.47 a#(a(x1)) -> a#(b(a(c(c(x1))))) -> a#(a(x1)) -> c#(c(x1)) 182.11/46.47 a#(a(x1)) -> a#(b(a(c(c(x1))))) -> a#(a(x1)) -> c#(x1) 182.11/46.47 a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> a#(b(a(c(c(x1))))) 182.11/46.47 a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> a#(c(c(x1))) 182.11/46.47 a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> c#(c(x1)) 182.11/46.47 a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> c#(x1) 182.11/46.47 EDG Processor: 182.11/46.47 DPs: 182.11/46.47 a#(a(x1)) -> c#(x1) 182.11/46.47 a#(a(x1)) -> c#(c(x1)) 182.11/46.47 a#(a(x1)) -> a#(c(c(x1))) 182.11/46.47 a#(a(x1)) -> a#(b(a(c(c(x1))))) 182.11/46.47 c#(b(x1)) -> a#(x1) 182.11/46.47 TRS: 182.11/46.47 a(a(x1)) -> a(b(a(c(c(x1))))) 182.11/46.47 c(a(x1)) -> x1 182.11/46.47 c(b(x1)) -> a(x1) 182.11/46.47 graph: 182.11/46.47 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(x1) 182.11/46.47 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(c(x1)) 182.11/46.47 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(c(c(x1))) 182.11/46.47 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(a(c(c(x1))))) 182.11/46.47 a#(a(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(x1) 182.11/46.47 a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(x1) 182.11/46.47 a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> c#(x1) 182.11/46.47 a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> c#(c(x1)) 182.11/46.47 a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> a#(c(c(x1))) 182.11/46.47 a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> a#(b(a(c(c(x1))))) 182.11/46.47 SCC Processor: 182.11/46.47 #sccs: 1 182.11/46.47 #rules: 4 182.11/46.47 #arcs: 10/25 182.11/46.47 DPs: 182.11/46.47 c#(b(x1)) -> a#(x1) 182.11/46.47 a#(a(x1)) -> a#(c(c(x1))) 182.11/46.47 a#(a(x1)) -> c#(c(x1)) 182.11/46.47 a#(a(x1)) -> c#(x1) 182.11/46.47 TRS: 182.11/46.47 a(a(x1)) -> a(b(a(c(c(x1))))) 182.11/46.47 c(a(x1)) -> x1 182.11/46.47 c(b(x1)) -> a(x1) 182.11/46.47 Arctic Interpretation Processor: 182.11/46.47 dimension: 2 182.11/46.47 usable rules: 182.11/46.47 a(a(x1)) -> a(b(a(c(c(x1))))) 182.11/46.47 c(a(x1)) -> x1 182.11/46.47 c(b(x1)) -> a(x1) 182.11/46.47 interpretation: 182.11/46.47 [c#](x0) = [-& 0 ]x0 + [1], 182.11/46.47 182.11/46.47 [a#](x0) = [-& 0 ]x0 + [0], 182.11/46.47 182.11/46.47 [0 1] [2] 182.11/46.47 [b](x0) = [0 0]x0 + [0], 182.11/46.47 182.11/46.47 [-& 0 ] [0] 182.11/46.47 [c](x0) = [0 -&]x0 + [0], 182.11/46.47 182.11/46.47 [-& 0 ] [0] 182.11/46.47 [a](x0) = [0 1 ]x0 + [1] 182.11/46.47 orientation: 182.11/46.47 c#(b(x1)) = [0 0]x1 + [1] >= [-& 0 ]x1 + [0] = a#(x1) 182.11/46.47 182.11/46.47 a#(a(x1)) = [0 1]x1 + [1] >= [-& 0 ]x1 + [0] = a#(c(c(x1))) 182.11/46.47 182.11/46.47 a#(a(x1)) = [0 1]x1 + [1] >= [0 -&]x1 + [1] = c#(c(x1)) 182.11/46.47 182.11/46.47 a#(a(x1)) = [0 1]x1 + [1] >= [-& 0 ]x1 + [1] = c#(x1) 182.11/46.47 182.11/46.47 [0 1] [1] [0 1] [1] 182.11/46.47 a(a(x1)) = [1 2]x1 + [2] >= [1 2]x1 + [2] = a(b(a(c(c(x1))))) 182.11/46.47 182.11/46.47 [0 1 ] [1] 182.11/46.47 c(a(x1)) = [-& 0 ]x1 + [0] >= x1 = x1 182.11/46.47 182.11/46.47 [0 0] [0] [-& 0 ] [0] 182.11/46.47 c(b(x1)) = [0 1]x1 + [2] >= [0 1 ]x1 + [1] = a(x1) 182.11/46.47 problem: 182.11/46.47 DPs: 182.11/46.47 c#(b(x1)) -> a#(x1) 182.11/46.47 a#(a(x1)) -> c#(c(x1)) 182.11/46.47 a#(a(x1)) -> c#(x1) 182.11/46.47 TRS: 182.11/46.47 a(a(x1)) -> a(b(a(c(c(x1))))) 182.11/46.47 c(a(x1)) -> x1 182.11/46.47 c(b(x1)) -> a(x1) 182.11/46.47 Restore Modifier: 182.11/46.47 DPs: 182.11/46.47 c#(b(x1)) -> a#(x1) 182.11/46.47 a#(a(x1)) -> c#(c(x1)) 182.11/46.47 a#(a(x1)) -> c#(x1) 182.11/46.47 TRS: 182.11/46.47 a(a(x1)) -> a(b(a(c(c(x1))))) 182.11/46.47 c(a(x1)) -> x1 182.11/46.47 c(b(x1)) -> a(x1) 182.11/46.47 EDG Processor: 182.11/46.47 DPs: 182.11/46.47 c#(b(x1)) -> a#(x1) 182.11/46.47 a#(a(x1)) -> c#(c(x1)) 182.11/46.47 a#(a(x1)) -> c#(x1) 182.11/46.47 TRS: 182.11/46.47 a(a(x1)) -> a(b(a(c(c(x1))))) 182.11/46.47 c(a(x1)) -> x1 182.11/46.47 c(b(x1)) -> a(x1) 182.11/46.47 graph: 182.11/46.47 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(c(x1)) 182.11/46.47 c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(x1) 182.11/46.47 a#(a(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(x1) 182.11/46.47 a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(x1) 182.11/46.47 Bounds Processor: 182.11/46.47 bound: 0 182.11/46.47 enrichment: match-dp 182.11/46.47 automaton: 182.11/46.47 final states: {1} 182.11/46.47 transitions: 182.11/46.47 c{#,0}(9) -> 10* 182.11/46.47 c{#,0}(18) -> 19* 182.11/46.47 c0(45) -> 46* 182.11/46.47 c0(31) -> 32* 182.11/46.47 c0(8) -> 9* 182.11/46.47 a0(32) -> 33* 182.11/46.47 a0(27) -> 28* 182.11/46.47 a0(34) -> 35* 182.11/46.47 f50() -> 2* 182.11/46.47 b0(33) -> 34* 182.11/46.47 a{#,0}(2) -> 1* 182.11/46.47 1 -> 10,19 182.11/46.47 2 -> 27,9,18,8 182.11/46.47 9 -> 31* 182.11/46.47 10 -> 1* 182.11/46.47 19 -> 1* 182.11/46.47 27 -> 32* 182.11/46.47 28 -> 32,9 182.11/46.47 32 -> 46,31,45 182.11/46.47 33 -> 28* 182.11/46.47 34 -> 32* 182.11/46.47 35 -> 9* 182.11/46.47 46 -> 31* 182.11/46.47 problem: 182.11/46.47 DPs: 182.11/46.47 a#(a(x1)) -> c#(c(x1)) 182.11/46.47 a#(a(x1)) -> c#(x1) 182.11/46.47 TRS: 182.11/46.47 a(a(x1)) -> a(b(a(c(c(x1))))) 182.11/46.47 c(a(x1)) -> x1 182.11/46.47 c(b(x1)) -> a(x1) 182.11/46.47 Restore Modifier: 182.11/46.47 DPs: 182.11/46.47 a#(a(x1)) -> c#(c(x1)) 182.11/46.47 a#(a(x1)) -> c#(x1) 182.11/46.47 TRS: 182.11/46.47 a(a(x1)) -> a(b(a(c(c(x1))))) 182.11/46.47 c(a(x1)) -> x1 182.11/46.47 c(b(x1)) -> a(x1) 182.11/46.47 EDG Processor: 182.11/46.47 DPs: 182.11/46.47 a#(a(x1)) -> c#(c(x1)) 182.11/46.47 a#(a(x1)) -> c#(x1) 182.11/46.47 TRS: 182.11/46.47 a(a(x1)) -> a(b(a(c(c(x1))))) 182.11/46.47 c(a(x1)) -> x1 182.11/46.47 c(b(x1)) -> a(x1) 182.11/46.47 graph: 182.11/46.47 182.11/46.47 SCC Processor: 182.11/46.47 #sccs: 0 182.11/46.47 #rules: 0 182.11/46.47 #arcs: 0/4 182.11/46.47 182.11/46.47 EOF