213.26/216.92 YES 213.26/216.92 213.26/216.92 Problem 1: 213.26/216.92 213.26/216.92 (VAR v_NonEmpty:S x1:S) 213.26/216.92 (RULES 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 ) 213.26/216.92 213.26/216.92 Problem 1: 213.26/216.92 213.26/216.92 Dependency Pairs Processor: 213.26/216.92 -> Pairs: 213.26/216.92 0#(3(x1:S)) -> 5#(3(x1:S)) 213.26/216.92 2#(4(x1:S)) -> 0#(7(x1:S)) 213.26/216.92 2#(4(x1:S)) -> 7#(x1:S) 213.26/216.92 2#(8(x1:S)) -> 4#(x1:S) 213.26/216.92 2#(8(x1:S)) -> 7#(x1:S) 213.26/216.92 4#(x1:S) -> 6#(6(x1:S)) 213.26/216.92 4#(x1:S) -> 6#(x1:S) 213.26/216.92 4#(x1:S) -> 9#(6(6(x1:S))) 213.26/216.92 5#(2(6(x1:S))) -> 2#(4(x1:S)) 213.26/216.92 5#(2(6(x1:S))) -> 4#(x1:S) 213.26/216.92 5#(2(6(x1:S))) -> 6#(2(4(x1:S))) 213.26/216.92 5#(9(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 6#(0(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(7(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(x1:S) 213.26/216.92 7#(0(x1:S)) -> 9#(3(x1:S)) 213.26/216.92 7#(2(x1:S)) -> 4#(x1:S) 213.26/216.92 9#(5(9(x1:S))) -> 5#(7(x1:S)) 213.26/216.92 9#(5(9(x1:S))) -> 7#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 5#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 7#(5(x1:S)) 213.26/216.92 9#(x1:S) -> 6#(7(x1:S)) 213.26/216.92 9#(x1:S) -> 7#(x1:S) 213.26/216.92 -> Rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 213.26/216.92 Problem 1: 213.26/216.92 213.26/216.92 SCC Processor: 213.26/216.92 -> Pairs: 213.26/216.92 0#(3(x1:S)) -> 5#(3(x1:S)) 213.26/216.92 2#(4(x1:S)) -> 0#(7(x1:S)) 213.26/216.92 2#(4(x1:S)) -> 7#(x1:S) 213.26/216.92 2#(8(x1:S)) -> 4#(x1:S) 213.26/216.92 2#(8(x1:S)) -> 7#(x1:S) 213.26/216.92 4#(x1:S) -> 6#(6(x1:S)) 213.26/216.92 4#(x1:S) -> 6#(x1:S) 213.26/216.92 4#(x1:S) -> 9#(6(6(x1:S))) 213.26/216.92 5#(2(6(x1:S))) -> 2#(4(x1:S)) 213.26/216.92 5#(2(6(x1:S))) -> 4#(x1:S) 213.26/216.92 5#(2(6(x1:S))) -> 6#(2(4(x1:S))) 213.26/216.92 5#(9(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 6#(0(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(7(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(x1:S) 213.26/216.92 7#(0(x1:S)) -> 9#(3(x1:S)) 213.26/216.92 7#(2(x1:S)) -> 4#(x1:S) 213.26/216.92 9#(5(9(x1:S))) -> 5#(7(x1:S)) 213.26/216.92 9#(5(9(x1:S))) -> 7#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 5#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 7#(5(x1:S)) 213.26/216.92 9#(x1:S) -> 6#(7(x1:S)) 213.26/216.92 9#(x1:S) -> 7#(x1:S) 213.26/216.92 -> Rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 ->Strongly Connected Components: 213.26/216.92 ->->Cycle: 213.26/216.92 ->->-> Pairs: 213.26/216.92 0#(3(x1:S)) -> 5#(3(x1:S)) 213.26/216.92 2#(4(x1:S)) -> 0#(7(x1:S)) 213.26/216.92 2#(4(x1:S)) -> 7#(x1:S) 213.26/216.92 2#(8(x1:S)) -> 4#(x1:S) 213.26/216.92 2#(8(x1:S)) -> 7#(x1:S) 213.26/216.92 4#(x1:S) -> 6#(6(x1:S)) 213.26/216.92 4#(x1:S) -> 6#(x1:S) 213.26/216.92 4#(x1:S) -> 9#(6(6(x1:S))) 213.26/216.92 5#(2(6(x1:S))) -> 2#(4(x1:S)) 213.26/216.92 5#(2(6(x1:S))) -> 4#(x1:S) 213.26/216.92 5#(2(6(x1:S))) -> 6#(2(4(x1:S))) 213.26/216.92 5#(9(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 6#(0(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(7(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(x1:S) 213.26/216.92 7#(0(x1:S)) -> 9#(3(x1:S)) 213.26/216.92 7#(2(x1:S)) -> 4#(x1:S) 213.26/216.92 9#(5(9(x1:S))) -> 5#(7(x1:S)) 213.26/216.92 9#(5(9(x1:S))) -> 7#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 5#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 7#(5(x1:S)) 213.26/216.92 9#(x1:S) -> 6#(7(x1:S)) 213.26/216.92 9#(x1:S) -> 7#(x1:S) 213.26/216.92 ->->-> Rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 213.26/216.92 Problem 1: 213.26/216.92 213.26/216.92 Reduction Pair Processor: 213.26/216.92 -> Pairs: 213.26/216.92 0#(3(x1:S)) -> 5#(3(x1:S)) 213.26/216.92 2#(4(x1:S)) -> 0#(7(x1:S)) 213.26/216.92 2#(4(x1:S)) -> 7#(x1:S) 213.26/216.92 2#(8(x1:S)) -> 4#(x1:S) 213.26/216.92 2#(8(x1:S)) -> 7#(x1:S) 213.26/216.92 4#(x1:S) -> 6#(6(x1:S)) 213.26/216.92 4#(x1:S) -> 6#(x1:S) 213.26/216.92 4#(x1:S) -> 9#(6(6(x1:S))) 213.26/216.92 5#(2(6(x1:S))) -> 2#(4(x1:S)) 213.26/216.92 5#(2(6(x1:S))) -> 4#(x1:S) 213.26/216.92 5#(2(6(x1:S))) -> 6#(2(4(x1:S))) 213.26/216.92 5#(9(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 6#(0(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(7(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(x1:S) 213.26/216.92 7#(0(x1:S)) -> 9#(3(x1:S)) 213.26/216.92 7#(2(x1:S)) -> 4#(x1:S) 213.26/216.92 9#(5(9(x1:S))) -> 5#(7(x1:S)) 213.26/216.92 9#(5(9(x1:S))) -> 7#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 5#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 7#(5(x1:S)) 213.26/216.92 9#(x1:S) -> 6#(7(x1:S)) 213.26/216.92 9#(x1:S) -> 7#(x1:S) 213.26/216.92 -> Rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 -> Usable rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 ->Interpretation type: 213.26/216.92 Linear 213.26/216.92 ->Coefficients: 213.26/216.92 Natural Numbers 213.26/216.92 ->Dimension: 213.26/216.92 1 213.26/216.92 ->Bound: 213.26/216.92 2 213.26/216.92 ->Interpretation: 213.26/216.92 213.26/216.92 [0](X) = 0 213.26/216.92 [2](X) = 2.X 213.26/216.92 [4](X) = 0 213.26/216.92 [5](X) = 0 213.26/216.92 [6](X) = 0 213.26/216.92 [7](X) = 0 213.26/216.92 [9](X) = 0 213.26/216.92 [1](X) = 0 213.26/216.92 [3](X) = 0 213.26/216.92 [8](X) = 2 213.26/216.92 [0#](X) = 2 213.26/216.92 [2#](X) = 2.X + 2 213.26/216.92 [4#](X) = 2 213.26/216.92 [5#](X) = 2 213.26/216.92 [6#](X) = 2 213.26/216.92 [7#](X) = 2 213.26/216.92 [9#](X) = 2.X + 2 213.26/216.92 213.26/216.92 Problem 1: 213.26/216.92 213.26/216.92 SCC Processor: 213.26/216.92 -> Pairs: 213.26/216.92 0#(3(x1:S)) -> 5#(3(x1:S)) 213.26/216.92 2#(4(x1:S)) -> 0#(7(x1:S)) 213.26/216.92 2#(4(x1:S)) -> 7#(x1:S) 213.26/216.92 2#(8(x1:S)) -> 7#(x1:S) 213.26/216.92 4#(x1:S) -> 6#(6(x1:S)) 213.26/216.92 4#(x1:S) -> 6#(x1:S) 213.26/216.92 4#(x1:S) -> 9#(6(6(x1:S))) 213.26/216.92 5#(2(6(x1:S))) -> 2#(4(x1:S)) 213.26/216.92 5#(2(6(x1:S))) -> 4#(x1:S) 213.26/216.92 5#(2(6(x1:S))) -> 6#(2(4(x1:S))) 213.26/216.92 5#(9(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 6#(0(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(7(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(x1:S) 213.26/216.92 7#(0(x1:S)) -> 9#(3(x1:S)) 213.26/216.92 7#(2(x1:S)) -> 4#(x1:S) 213.26/216.92 9#(5(9(x1:S))) -> 5#(7(x1:S)) 213.26/216.92 9#(5(9(x1:S))) -> 7#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 5#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 7#(5(x1:S)) 213.26/216.92 9#(x1:S) -> 6#(7(x1:S)) 213.26/216.92 9#(x1:S) -> 7#(x1:S) 213.26/216.92 -> Rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 ->Strongly Connected Components: 213.26/216.92 ->->Cycle: 213.26/216.92 ->->-> Pairs: 213.26/216.92 0#(3(x1:S)) -> 5#(3(x1:S)) 213.26/216.92 2#(4(x1:S)) -> 0#(7(x1:S)) 213.26/216.92 2#(4(x1:S)) -> 7#(x1:S) 213.26/216.92 2#(8(x1:S)) -> 7#(x1:S) 213.26/216.92 4#(x1:S) -> 6#(6(x1:S)) 213.26/216.92 4#(x1:S) -> 6#(x1:S) 213.26/216.92 4#(x1:S) -> 9#(6(6(x1:S))) 213.26/216.92 5#(2(6(x1:S))) -> 2#(4(x1:S)) 213.26/216.92 5#(2(6(x1:S))) -> 4#(x1:S) 213.26/216.92 5#(2(6(x1:S))) -> 6#(2(4(x1:S))) 213.26/216.92 5#(9(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 6#(0(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(7(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(x1:S) 213.26/216.92 7#(0(x1:S)) -> 9#(3(x1:S)) 213.26/216.92 7#(2(x1:S)) -> 4#(x1:S) 213.26/216.92 9#(5(9(x1:S))) -> 5#(7(x1:S)) 213.26/216.92 9#(5(9(x1:S))) -> 7#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 5#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 7#(5(x1:S)) 213.26/216.92 9#(x1:S) -> 6#(7(x1:S)) 213.26/216.92 9#(x1:S) -> 7#(x1:S) 213.26/216.92 ->->-> Rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 213.26/216.92 Problem 1: 213.26/216.92 213.26/216.92 Reduction Pair Processor: 213.26/216.92 -> Pairs: 213.26/216.92 0#(3(x1:S)) -> 5#(3(x1:S)) 213.26/216.92 2#(4(x1:S)) -> 0#(7(x1:S)) 213.26/216.92 2#(4(x1:S)) -> 7#(x1:S) 213.26/216.92 2#(8(x1:S)) -> 7#(x1:S) 213.26/216.92 4#(x1:S) -> 6#(6(x1:S)) 213.26/216.92 4#(x1:S) -> 6#(x1:S) 213.26/216.92 4#(x1:S) -> 9#(6(6(x1:S))) 213.26/216.92 5#(2(6(x1:S))) -> 2#(4(x1:S)) 213.26/216.92 5#(2(6(x1:S))) -> 4#(x1:S) 213.26/216.92 5#(2(6(x1:S))) -> 6#(2(4(x1:S))) 213.26/216.92 5#(9(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 6#(0(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(7(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(x1:S) 213.26/216.92 7#(0(x1:S)) -> 9#(3(x1:S)) 213.26/216.92 7#(2(x1:S)) -> 4#(x1:S) 213.26/216.92 9#(5(9(x1:S))) -> 5#(7(x1:S)) 213.26/216.92 9#(5(9(x1:S))) -> 7#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 5#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 7#(5(x1:S)) 213.26/216.92 9#(x1:S) -> 6#(7(x1:S)) 213.26/216.92 9#(x1:S) -> 7#(x1:S) 213.26/216.92 -> Rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 -> Usable rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 ->Interpretation type: 213.26/216.92 Linear 213.26/216.92 ->Coefficients: 213.26/216.92 Natural Numbers 213.26/216.92 ->Dimension: 213.26/216.92 1 213.26/216.92 ->Bound: 213.26/216.92 2 213.26/216.92 ->Interpretation: 213.26/216.92 213.26/216.92 [0](X) = 1 213.26/216.92 [2](X) = 2 213.26/216.92 [4](X) = 1 213.26/216.92 [5](X) = 1 213.26/216.92 [6](X) = 1 213.26/216.92 [7](X) = 1 213.26/216.92 [9](X) = 1 213.26/216.92 [1](X) = 1 213.26/216.92 [3](X) = 1 213.26/216.92 [8](X) = 2 213.26/216.92 [0#](X) = 2 213.26/216.92 [2#](X) = X + 1 213.26/216.92 [4#](X) = 2 213.26/216.92 [5#](X) = 2 213.26/216.92 [6#](X) = 2 213.26/216.92 [7#](X) = 2 213.26/216.92 [9#](X) = 2 213.26/216.92 213.26/216.92 Problem 1: 213.26/216.92 213.26/216.92 SCC Processor: 213.26/216.92 -> Pairs: 213.26/216.92 0#(3(x1:S)) -> 5#(3(x1:S)) 213.26/216.92 2#(4(x1:S)) -> 0#(7(x1:S)) 213.26/216.92 2#(4(x1:S)) -> 7#(x1:S) 213.26/216.92 4#(x1:S) -> 6#(6(x1:S)) 213.26/216.92 4#(x1:S) -> 6#(x1:S) 213.26/216.92 4#(x1:S) -> 9#(6(6(x1:S))) 213.26/216.92 5#(2(6(x1:S))) -> 2#(4(x1:S)) 213.26/216.92 5#(2(6(x1:S))) -> 4#(x1:S) 213.26/216.92 5#(2(6(x1:S))) -> 6#(2(4(x1:S))) 213.26/216.92 5#(9(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 6#(0(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(7(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(x1:S) 213.26/216.92 7#(0(x1:S)) -> 9#(3(x1:S)) 213.26/216.92 7#(2(x1:S)) -> 4#(x1:S) 213.26/216.92 9#(5(9(x1:S))) -> 5#(7(x1:S)) 213.26/216.92 9#(5(9(x1:S))) -> 7#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 5#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 7#(5(x1:S)) 213.26/216.92 9#(x1:S) -> 6#(7(x1:S)) 213.26/216.92 9#(x1:S) -> 7#(x1:S) 213.26/216.92 -> Rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 ->Strongly Connected Components: 213.26/216.92 ->->Cycle: 213.26/216.92 ->->-> Pairs: 213.26/216.92 0#(3(x1:S)) -> 5#(3(x1:S)) 213.26/216.92 2#(4(x1:S)) -> 0#(7(x1:S)) 213.26/216.92 2#(4(x1:S)) -> 7#(x1:S) 213.26/216.92 4#(x1:S) -> 6#(6(x1:S)) 213.26/216.92 4#(x1:S) -> 6#(x1:S) 213.26/216.92 4#(x1:S) -> 9#(6(6(x1:S))) 213.26/216.92 5#(2(6(x1:S))) -> 2#(4(x1:S)) 213.26/216.92 5#(2(6(x1:S))) -> 4#(x1:S) 213.26/216.92 5#(2(6(x1:S))) -> 6#(2(4(x1:S))) 213.26/216.92 5#(9(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 6#(0(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(7(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(x1:S) 213.26/216.92 7#(0(x1:S)) -> 9#(3(x1:S)) 213.26/216.92 7#(2(x1:S)) -> 4#(x1:S) 213.26/216.92 9#(5(9(x1:S))) -> 5#(7(x1:S)) 213.26/216.92 9#(5(9(x1:S))) -> 7#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 5#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 7#(5(x1:S)) 213.26/216.92 9#(x1:S) -> 6#(7(x1:S)) 213.26/216.92 9#(x1:S) -> 7#(x1:S) 213.26/216.92 ->->-> Rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 213.26/216.92 Problem 1: 213.26/216.92 213.26/216.92 Reduction Pair Processor: 213.26/216.92 -> Pairs: 213.26/216.92 0#(3(x1:S)) -> 5#(3(x1:S)) 213.26/216.92 2#(4(x1:S)) -> 0#(7(x1:S)) 213.26/216.92 2#(4(x1:S)) -> 7#(x1:S) 213.26/216.92 4#(x1:S) -> 6#(6(x1:S)) 213.26/216.92 4#(x1:S) -> 6#(x1:S) 213.26/216.92 4#(x1:S) -> 9#(6(6(x1:S))) 213.26/216.92 5#(2(6(x1:S))) -> 2#(4(x1:S)) 213.26/216.92 5#(2(6(x1:S))) -> 4#(x1:S) 213.26/216.92 5#(2(6(x1:S))) -> 6#(2(4(x1:S))) 213.26/216.92 5#(9(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 6#(0(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(7(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(x1:S) 213.26/216.92 7#(0(x1:S)) -> 9#(3(x1:S)) 213.26/216.92 7#(2(x1:S)) -> 4#(x1:S) 213.26/216.92 9#(5(9(x1:S))) -> 5#(7(x1:S)) 213.26/216.92 9#(5(9(x1:S))) -> 7#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 5#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 7#(5(x1:S)) 213.26/216.92 9#(x1:S) -> 6#(7(x1:S)) 213.26/216.92 9#(x1:S) -> 7#(x1:S) 213.26/216.92 -> Rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 -> Usable rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 ->Interpretation type: 213.26/216.92 Linear 213.26/216.92 ->Coefficients: 213.26/216.92 Natural Numbers 213.26/216.92 ->Dimension: 213.26/216.92 2 213.26/216.92 ->Bound: 213.26/216.92 1 213.26/216.92 ->Interpretation: 213.26/216.92 213.26/216.92 [0](X) = 0 213.26/216.92 [2](X) = [1 0;0 1].X + [0;1] 213.26/216.92 [4](X) = [1;0] 213.26/216.92 [5](X) = [0 1;0 0].X 213.26/216.92 [6](X) = 0 213.26/216.92 [7](X) = [0 1;0 0].X 213.26/216.92 [9](X) = 0 213.26/216.92 [1](X) = [0 0;0 1].X 213.26/216.92 [3](X) = 0 213.26/216.92 [8](X) = [0 1;0 0].X + [1;1] 213.26/216.92 [0#](X) = [1;1] 213.26/216.92 [2#](X) = [1 1;0 1].X + [1;1] 213.26/216.92 [4#](X) = [1;1] 213.26/216.92 [5#](X) = [0 1;0 0].X + [1;1] 213.26/216.92 [6#](X) = [1;1] 213.26/216.92 [7#](X) = [1;1] 213.26/216.92 [9#](X) = [1 0;0 0].X + [1;1] 213.26/216.92 213.26/216.92 Problem 1: 213.26/216.92 213.26/216.92 SCC Processor: 213.26/216.92 -> Pairs: 213.26/216.92 0#(3(x1:S)) -> 5#(3(x1:S)) 213.26/216.92 2#(4(x1:S)) -> 7#(x1:S) 213.26/216.92 4#(x1:S) -> 6#(6(x1:S)) 213.26/216.92 4#(x1:S) -> 6#(x1:S) 213.26/216.92 4#(x1:S) -> 9#(6(6(x1:S))) 213.26/216.92 5#(2(6(x1:S))) -> 2#(4(x1:S)) 213.26/216.92 5#(2(6(x1:S))) -> 4#(x1:S) 213.26/216.92 5#(2(6(x1:S))) -> 6#(2(4(x1:S))) 213.26/216.92 5#(9(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 6#(0(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(7(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(x1:S) 213.26/216.92 7#(0(x1:S)) -> 9#(3(x1:S)) 213.26/216.92 7#(2(x1:S)) -> 4#(x1:S) 213.26/216.92 9#(5(9(x1:S))) -> 5#(7(x1:S)) 213.26/216.92 9#(5(9(x1:S))) -> 7#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 5#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 7#(5(x1:S)) 213.26/216.92 9#(x1:S) -> 6#(7(x1:S)) 213.26/216.92 9#(x1:S) -> 7#(x1:S) 213.26/216.92 -> Rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 ->Strongly Connected Components: 213.26/216.92 ->->Cycle: 213.26/216.92 ->->-> Pairs: 213.26/216.92 0#(3(x1:S)) -> 5#(3(x1:S)) 213.26/216.92 2#(4(x1:S)) -> 7#(x1:S) 213.26/216.92 4#(x1:S) -> 6#(6(x1:S)) 213.26/216.92 4#(x1:S) -> 6#(x1:S) 213.26/216.92 4#(x1:S) -> 9#(6(6(x1:S))) 213.26/216.92 5#(2(6(x1:S))) -> 2#(4(x1:S)) 213.26/216.92 5#(2(6(x1:S))) -> 4#(x1:S) 213.26/216.92 5#(2(6(x1:S))) -> 6#(2(4(x1:S))) 213.26/216.92 5#(9(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 6#(0(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(7(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(x1:S) 213.26/216.92 7#(0(x1:S)) -> 9#(3(x1:S)) 213.26/216.92 7#(2(x1:S)) -> 4#(x1:S) 213.26/216.92 9#(5(9(x1:S))) -> 5#(7(x1:S)) 213.26/216.92 9#(5(9(x1:S))) -> 7#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 5#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 7#(5(x1:S)) 213.26/216.92 9#(x1:S) -> 6#(7(x1:S)) 213.26/216.92 9#(x1:S) -> 7#(x1:S) 213.26/216.92 ->->-> Rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 213.26/216.92 Problem 1: 213.26/216.92 213.26/216.92 Reduction Pair Processor: 213.26/216.92 -> Pairs: 213.26/216.92 0#(3(x1:S)) -> 5#(3(x1:S)) 213.26/216.92 2#(4(x1:S)) -> 7#(x1:S) 213.26/216.92 4#(x1:S) -> 6#(6(x1:S)) 213.26/216.92 4#(x1:S) -> 6#(x1:S) 213.26/216.92 4#(x1:S) -> 9#(6(6(x1:S))) 213.26/216.92 5#(2(6(x1:S))) -> 2#(4(x1:S)) 213.26/216.92 5#(2(6(x1:S))) -> 4#(x1:S) 213.26/216.92 5#(2(6(x1:S))) -> 6#(2(4(x1:S))) 213.26/216.92 5#(9(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 6#(0(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(7(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(x1:S) 213.26/216.92 7#(0(x1:S)) -> 9#(3(x1:S)) 213.26/216.92 7#(2(x1:S)) -> 4#(x1:S) 213.26/216.92 9#(5(9(x1:S))) -> 5#(7(x1:S)) 213.26/216.92 9#(5(9(x1:S))) -> 7#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 5#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 7#(5(x1:S)) 213.26/216.92 9#(x1:S) -> 6#(7(x1:S)) 213.26/216.92 9#(x1:S) -> 7#(x1:S) 213.26/216.92 -> Rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 -> Usable rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 ->Interpretation type: 213.26/216.92 Linear 213.26/216.92 ->Coefficients: 213.26/216.92 Natural Numbers 213.26/216.92 ->Dimension: 213.26/216.92 2 213.26/216.92 ->Bound: 213.26/216.92 1 213.26/216.92 ->Interpretation: 213.26/216.92 213.26/216.92 [0](X) = 0 213.26/216.92 [2](X) = [0 0;0 1].X + [1;0] 213.26/216.92 [4](X) = [0;1] 213.26/216.92 [5](X) = 0 213.26/216.92 [6](X) = 0 213.26/216.92 [7](X) = [0 0;1 0].X 213.26/216.92 [9](X) = 0 213.26/216.92 [1](X) = [1 0;0 0].X 213.26/216.92 [3](X) = 0 213.26/216.92 [8](X) = [0 0;1 0].X + [1;1] 213.26/216.92 [0#](X) = [1;1] 213.26/216.92 [2#](X) = [1 1;0 1].X + [1;1] 213.26/216.92 [4#](X) = [1;1] 213.26/216.92 [5#](X) = [1 0;1 0].X + [1;1] 213.26/216.92 [6#](X) = [1;1] 213.26/216.92 [7#](X) = [1;1] 213.26/216.92 [9#](X) = [0 1;1 1].X + [1;1] 213.26/216.92 213.26/216.92 Problem 1: 213.26/216.92 213.26/216.92 SCC Processor: 213.26/216.92 -> Pairs: 213.26/216.92 0#(3(x1:S)) -> 5#(3(x1:S)) 213.26/216.92 4#(x1:S) -> 6#(6(x1:S)) 213.26/216.92 4#(x1:S) -> 6#(x1:S) 213.26/216.92 4#(x1:S) -> 9#(6(6(x1:S))) 213.26/216.92 5#(2(6(x1:S))) -> 2#(4(x1:S)) 213.26/216.92 5#(2(6(x1:S))) -> 4#(x1:S) 213.26/216.92 5#(2(6(x1:S))) -> 6#(2(4(x1:S))) 213.26/216.92 5#(9(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 6#(0(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(7(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(x1:S) 213.26/216.92 7#(0(x1:S)) -> 9#(3(x1:S)) 213.26/216.92 7#(2(x1:S)) -> 4#(x1:S) 213.26/216.92 9#(5(9(x1:S))) -> 5#(7(x1:S)) 213.26/216.92 9#(5(9(x1:S))) -> 7#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 5#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 7#(5(x1:S)) 213.26/216.92 9#(x1:S) -> 6#(7(x1:S)) 213.26/216.92 9#(x1:S) -> 7#(x1:S) 213.26/216.92 -> Rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 ->Strongly Connected Components: 213.26/216.92 ->->Cycle: 213.26/216.92 ->->-> Pairs: 213.26/216.92 0#(3(x1:S)) -> 5#(3(x1:S)) 213.26/216.92 4#(x1:S) -> 6#(6(x1:S)) 213.26/216.92 4#(x1:S) -> 6#(x1:S) 213.26/216.92 4#(x1:S) -> 9#(6(6(x1:S))) 213.26/216.92 5#(2(6(x1:S))) -> 4#(x1:S) 213.26/216.92 5#(2(6(x1:S))) -> 6#(2(4(x1:S))) 213.26/216.92 5#(9(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 6#(0(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(7(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(x1:S) 213.26/216.92 7#(0(x1:S)) -> 9#(3(x1:S)) 213.26/216.92 7#(2(x1:S)) -> 4#(x1:S) 213.26/216.92 9#(5(9(x1:S))) -> 5#(7(x1:S)) 213.26/216.92 9#(5(9(x1:S))) -> 7#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 5#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 7#(5(x1:S)) 213.26/216.92 9#(x1:S) -> 6#(7(x1:S)) 213.26/216.92 9#(x1:S) -> 7#(x1:S) 213.26/216.92 ->->-> Rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 213.26/216.92 Problem 1: 213.26/216.92 213.26/216.92 Reduction Pair Processor: 213.26/216.92 -> Pairs: 213.26/216.92 0#(3(x1:S)) -> 5#(3(x1:S)) 213.26/216.92 4#(x1:S) -> 6#(6(x1:S)) 213.26/216.92 4#(x1:S) -> 6#(x1:S) 213.26/216.92 4#(x1:S) -> 9#(6(6(x1:S))) 213.26/216.92 5#(2(6(x1:S))) -> 4#(x1:S) 213.26/216.92 5#(2(6(x1:S))) -> 6#(2(4(x1:S))) 213.26/216.92 5#(9(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 6#(0(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(7(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(x1:S) 213.26/216.92 7#(0(x1:S)) -> 9#(3(x1:S)) 213.26/216.92 7#(2(x1:S)) -> 4#(x1:S) 213.26/216.92 9#(5(9(x1:S))) -> 5#(7(x1:S)) 213.26/216.92 9#(5(9(x1:S))) -> 7#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 5#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 7#(5(x1:S)) 213.26/216.92 9#(x1:S) -> 6#(7(x1:S)) 213.26/216.92 9#(x1:S) -> 7#(x1:S) 213.26/216.92 -> Rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 -> Usable rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 ->Interpretation type: 213.26/216.92 Linear 213.26/216.92 ->Coefficients: 213.26/216.92 Natural Numbers 213.26/216.92 ->Dimension: 213.26/216.92 2 213.26/216.92 ->Bound: 213.26/216.92 1 213.26/216.92 ->Interpretation: 213.26/216.92 213.26/216.92 [0](X) = [1;0] 213.26/216.92 [2](X) = [1 1;1 0].X + [0;1] 213.26/216.92 [4](X) = [1 0;0 0].X + [1;0] 213.26/216.92 [5](X) = [1 0;0 0].X + [1;0] 213.26/216.92 [6](X) = [1 0;0 0].X 213.26/216.92 [7](X) = [1 1;0 0].X 213.26/216.92 [9](X) = [1 1;0 0].X + [1;0] 213.26/216.92 [1](X) = [0 1;1 1].X 213.26/216.92 [3](X) = 0 213.26/216.92 [8](X) = [1 1;0 0].X + [1;0] 213.26/216.92 [0#](X) = [1;1] 213.26/216.92 [4#](X) = [1 0;0 0].X + [1;1] 213.26/216.92 [5#](X) = [1 1;0 0].X + [1;1] 213.26/216.92 [6#](X) = [1 0;0 0].X + [0;1] 213.26/216.92 [7#](X) = [1 1;0 0].X + [0;1] 213.26/216.92 [9#](X) = [1 1;0 0].X + [1;1] 213.26/216.92 213.26/216.92 Problem 1: 213.26/216.92 213.26/216.92 SCC Processor: 213.26/216.92 -> Pairs: 213.26/216.92 0#(3(x1:S)) -> 5#(3(x1:S)) 213.26/216.92 4#(x1:S) -> 6#(x1:S) 213.26/216.92 4#(x1:S) -> 9#(6(6(x1:S))) 213.26/216.92 5#(2(6(x1:S))) -> 4#(x1:S) 213.26/216.92 5#(2(6(x1:S))) -> 6#(2(4(x1:S))) 213.26/216.92 5#(9(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 6#(0(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(7(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(x1:S) 213.26/216.92 7#(0(x1:S)) -> 9#(3(x1:S)) 213.26/216.92 7#(2(x1:S)) -> 4#(x1:S) 213.26/216.92 9#(5(9(x1:S))) -> 5#(7(x1:S)) 213.26/216.92 9#(5(9(x1:S))) -> 7#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 5#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 7#(5(x1:S)) 213.26/216.92 9#(x1:S) -> 6#(7(x1:S)) 213.26/216.92 9#(x1:S) -> 7#(x1:S) 213.26/216.92 -> Rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 ->Strongly Connected Components: 213.26/216.92 ->->Cycle: 213.26/216.92 ->->-> Pairs: 213.26/216.92 0#(3(x1:S)) -> 5#(3(x1:S)) 213.26/216.92 4#(x1:S) -> 6#(x1:S) 213.26/216.92 4#(x1:S) -> 9#(6(6(x1:S))) 213.26/216.92 5#(2(6(x1:S))) -> 4#(x1:S) 213.26/216.92 5#(2(6(x1:S))) -> 6#(2(4(x1:S))) 213.26/216.92 5#(9(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 6#(0(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(7(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(x1:S) 213.26/216.92 7#(0(x1:S)) -> 9#(3(x1:S)) 213.26/216.92 7#(2(x1:S)) -> 4#(x1:S) 213.26/216.92 9#(5(9(x1:S))) -> 5#(7(x1:S)) 213.26/216.92 9#(5(9(x1:S))) -> 7#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 5#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 7#(5(x1:S)) 213.26/216.92 9#(x1:S) -> 6#(7(x1:S)) 213.26/216.92 9#(x1:S) -> 7#(x1:S) 213.26/216.92 ->->-> Rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 213.26/216.92 Problem 1: 213.26/216.92 213.26/216.92 Reduction Pair Processor: 213.26/216.92 -> Pairs: 213.26/216.92 0#(3(x1:S)) -> 5#(3(x1:S)) 213.26/216.92 4#(x1:S) -> 6#(x1:S) 213.26/216.92 4#(x1:S) -> 9#(6(6(x1:S))) 213.26/216.92 5#(2(6(x1:S))) -> 4#(x1:S) 213.26/216.92 5#(2(6(x1:S))) -> 6#(2(4(x1:S))) 213.26/216.92 5#(9(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 6#(0(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(7(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(x1:S) 213.26/216.92 7#(0(x1:S)) -> 9#(3(x1:S)) 213.26/216.92 7#(2(x1:S)) -> 4#(x1:S) 213.26/216.92 9#(5(9(x1:S))) -> 5#(7(x1:S)) 213.26/216.92 9#(5(9(x1:S))) -> 7#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 5#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 7#(5(x1:S)) 213.26/216.92 9#(x1:S) -> 6#(7(x1:S)) 213.26/216.92 9#(x1:S) -> 7#(x1:S) 213.26/216.92 -> Rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 -> Usable rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 ->Interpretation type: 213.26/216.92 Linear 213.26/216.92 ->Coefficients: 213.26/216.92 Natural Numbers 213.26/216.92 ->Dimension: 213.26/216.92 2 213.26/216.92 ->Bound: 213.26/216.92 1 213.26/216.92 ->Interpretation: 213.26/216.92 213.26/216.92 [0](X) = [1;0] 213.26/216.92 [2](X) = [1 1;1 1].X + [0;1] 213.26/216.92 [4](X) = [0 0;0 1].X + [1;1] 213.26/216.92 [5](X) = [0 0;1 1].X + [1;0] 213.26/216.92 [6](X) = [0 0;0 1].X + [1;0] 213.26/216.92 [7](X) = [0 0;1 1].X + [1;0] 213.26/216.92 [9](X) = [0 0;1 1].X + [1;0] 213.26/216.92 [1](X) = [1 1;1 0].X + [0;1] 213.26/216.92 [3](X) = 0 213.26/216.92 [8](X) = [1 1;0 0].X + [0;1] 213.26/216.92 [0#](X) = [1;1] 213.26/216.92 [4#](X) = [0 1;0 1].X + [1;1] 213.26/216.92 [5#](X) = [1 1;0 1].X + [1;1] 213.26/216.92 [6#](X) = [0 1;0 1].X 213.26/216.92 [7#](X) = [0 1;1 1].X 213.26/216.92 [9#](X) = [1 1;1 1].X 213.26/216.92 213.26/216.92 Problem 1: 213.26/216.92 213.26/216.92 SCC Processor: 213.26/216.92 -> Pairs: 213.26/216.92 0#(3(x1:S)) -> 5#(3(x1:S)) 213.26/216.92 4#(x1:S) -> 9#(6(6(x1:S))) 213.26/216.92 5#(2(6(x1:S))) -> 4#(x1:S) 213.26/216.92 5#(2(6(x1:S))) -> 6#(2(4(x1:S))) 213.26/216.92 5#(9(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 6#(0(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(7(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(x1:S) 213.26/216.92 7#(0(x1:S)) -> 9#(3(x1:S)) 213.26/216.92 7#(2(x1:S)) -> 4#(x1:S) 213.26/216.92 9#(5(9(x1:S))) -> 5#(7(x1:S)) 213.26/216.92 9#(5(9(x1:S))) -> 7#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 5#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 7#(5(x1:S)) 213.26/216.92 9#(x1:S) -> 6#(7(x1:S)) 213.26/216.92 9#(x1:S) -> 7#(x1:S) 213.26/216.92 -> Rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 ->Strongly Connected Components: 213.26/216.92 ->->Cycle: 213.26/216.92 ->->-> Pairs: 213.26/216.92 0#(3(x1:S)) -> 5#(3(x1:S)) 213.26/216.92 4#(x1:S) -> 9#(6(6(x1:S))) 213.26/216.92 5#(2(6(x1:S))) -> 4#(x1:S) 213.26/216.92 5#(2(6(x1:S))) -> 6#(2(4(x1:S))) 213.26/216.92 5#(9(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 6#(0(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(7(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(x1:S) 213.26/216.92 7#(0(x1:S)) -> 9#(3(x1:S)) 213.26/216.92 7#(2(x1:S)) -> 4#(x1:S) 213.26/216.92 9#(5(9(x1:S))) -> 5#(7(x1:S)) 213.26/216.92 9#(5(9(x1:S))) -> 7#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 5#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 7#(5(x1:S)) 213.26/216.92 9#(x1:S) -> 6#(7(x1:S)) 213.26/216.92 9#(x1:S) -> 7#(x1:S) 213.26/216.92 ->->-> Rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 213.26/216.92 Problem 1: 213.26/216.92 213.26/216.92 Reduction Pair Processor: 213.26/216.92 -> Pairs: 213.26/216.92 0#(3(x1:S)) -> 5#(3(x1:S)) 213.26/216.92 4#(x1:S) -> 9#(6(6(x1:S))) 213.26/216.92 5#(2(6(x1:S))) -> 4#(x1:S) 213.26/216.92 5#(2(6(x1:S))) -> 6#(2(4(x1:S))) 213.26/216.92 5#(9(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 6#(0(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(7(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(x1:S) 213.26/216.92 7#(0(x1:S)) -> 9#(3(x1:S)) 213.26/216.92 7#(2(x1:S)) -> 4#(x1:S) 213.26/216.92 9#(5(9(x1:S))) -> 5#(7(x1:S)) 213.26/216.92 9#(5(9(x1:S))) -> 7#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 5#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 7#(5(x1:S)) 213.26/216.92 9#(x1:S) -> 6#(7(x1:S)) 213.26/216.92 9#(x1:S) -> 7#(x1:S) 213.26/216.92 -> Rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 -> Usable rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 ->Interpretation type: 213.26/216.92 Linear 213.26/216.92 ->Coefficients: 213.26/216.92 Natural Numbers 213.26/216.92 ->Dimension: 213.26/216.92 1 213.26/216.92 ->Bound: 213.26/216.92 2 213.26/216.92 ->Interpretation: 213.26/216.92 213.26/216.92 [0](X) = 0 213.26/216.92 [2](X) = 2.X + 1 213.26/216.92 [4](X) = 0 213.26/216.92 [5](X) = 0 213.26/216.92 [6](X) = 0 213.26/216.92 [7](X) = 0 213.26/216.92 [9](X) = 0 213.26/216.92 [1](X) = 0 213.26/216.92 [3](X) = 0 213.26/216.92 [8](X) = 1 213.26/216.92 [0#](X) = 2 213.26/216.92 [4#](X) = 2 213.26/216.92 [5#](X) = 2 213.26/216.92 [6#](X) = 2.X 213.26/216.92 [7#](X) = 2 213.26/216.92 [9#](X) = 2 213.26/216.92 213.26/216.92 Problem 1: 213.26/216.92 213.26/216.92 SCC Processor: 213.26/216.92 -> Pairs: 213.26/216.92 0#(3(x1:S)) -> 5#(3(x1:S)) 213.26/216.92 4#(x1:S) -> 9#(6(6(x1:S))) 213.26/216.92 5#(2(6(x1:S))) -> 4#(x1:S) 213.26/216.92 5#(2(6(x1:S))) -> 6#(2(4(x1:S))) 213.26/216.92 5#(9(x1:S)) -> 0#(x1:S) 213.26/216.92 5#(3(x1:S)) -> 0#(x1:S) 213.26/216.92 6#(2(x1:S)) -> 7#(7(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(x1:S) 213.26/216.92 7#(0(x1:S)) -> 9#(3(x1:S)) 213.26/216.92 7#(2(x1:S)) -> 4#(x1:S) 213.26/216.92 9#(5(9(x1:S))) -> 5#(7(x1:S)) 213.26/216.92 9#(5(9(x1:S))) -> 7#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 5#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 7#(5(x1:S)) 213.26/216.92 9#(x1:S) -> 6#(7(x1:S)) 213.26/216.92 9#(x1:S) -> 7#(x1:S) 213.26/216.92 -> Rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 ->Strongly Connected Components: 213.26/216.92 ->->Cycle: 213.26/216.92 ->->-> Pairs: 213.26/216.92 0#(3(x1:S)) -> 5#(3(x1:S)) 213.26/216.92 5#(3(x1:S)) -> 0#(x1:S) 213.26/216.92 ->->-> Rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 ->->Cycle: 213.26/216.92 ->->-> Pairs: 213.26/216.92 4#(x1:S) -> 9#(6(6(x1:S))) 213.26/216.92 5#(2(6(x1:S))) -> 4#(x1:S) 213.26/216.92 5#(2(6(x1:S))) -> 6#(2(4(x1:S))) 213.26/216.92 6#(2(x1:S)) -> 7#(7(x1:S)) 213.26/216.92 6#(2(x1:S)) -> 7#(x1:S) 213.26/216.92 7#(0(x1:S)) -> 9#(3(x1:S)) 213.26/216.92 7#(2(x1:S)) -> 4#(x1:S) 213.26/216.92 9#(5(9(x1:S))) -> 5#(7(x1:S)) 213.26/216.92 9#(5(9(x1:S))) -> 7#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 5#(x1:S) 213.26/216.92 9#(7(x1:S)) -> 7#(5(x1:S)) 213.26/216.92 9#(x1:S) -> 6#(7(x1:S)) 213.26/216.92 9#(x1:S) -> 7#(x1:S) 213.26/216.92 ->->-> Rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 213.26/216.92 213.26/216.92 The problem is decomposed in 2 subproblems. 213.26/216.92 213.26/216.92 Problem 1.1: 213.26/216.92 213.26/216.92 Subterm Processor: 213.26/216.92 -> Pairs: 213.26/216.92 0#(3(x1:S)) -> 5#(3(x1:S)) 213.26/216.92 5#(3(x1:S)) -> 0#(x1:S) 213.26/216.92 -> Rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 ->Projection: 213.26/216.92 pi(0#) = 1 213.26/216.92 pi(5#) = 1 213.26/216.92 213.26/216.92 Problem 1.1: 213.26/216.92 213.26/216.92 SCC Processor: 213.26/216.92 -> Pairs: 213.26/216.92 0#(3(x1:S)) -> 5#(3(x1:S)) 213.26/216.92 -> Rules: 213.26/216.92 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.92 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.92 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.92 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.92 2(8(x1:S)) -> 4(x1:S) 213.26/216.92 2(8(x1:S)) -> 7(x1:S) 213.26/216.92 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.92 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.92 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.92 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.92 5(9(x1:S)) -> 0(x1:S) 213.26/216.92 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.92 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.92 6(6(x1:S)) -> 3(x1:S) 213.26/216.92 6(9(x1:S)) -> 9(x1:S) 213.26/216.92 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.92 7(2(x1:S)) -> 4(x1:S) 213.26/216.92 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.92 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.92 9(x1:S) -> 6(7(x1:S)) 213.26/216.92 ->Strongly Connected Components: 213.26/216.92 There is no strongly connected component 213.26/216.92 213.26/216.92 The problem is finite. 213.26/216.92 213.26/216.92 Problem 1.2: 213.26/216.92 213.26/216.92 Reduction Pair Processor: 213.26/216.92 -> Pairs: 213.26/216.92 4#(x1:S) -> 9#(6(6(x1:S))) 213.26/216.92 5#(2(6(x1:S))) -> 4#(x1:S) 213.26/216.93 5#(2(6(x1:S))) -> 6#(2(4(x1:S))) 213.26/216.93 6#(2(x1:S)) -> 7#(7(x1:S)) 213.26/216.93 6#(2(x1:S)) -> 7#(x1:S) 213.26/216.93 7#(0(x1:S)) -> 9#(3(x1:S)) 213.26/216.93 7#(2(x1:S)) -> 4#(x1:S) 213.26/216.93 9#(5(9(x1:S))) -> 5#(7(x1:S)) 213.26/216.93 9#(5(9(x1:S))) -> 7#(x1:S) 213.26/216.93 9#(7(x1:S)) -> 5#(x1:S) 213.26/216.93 9#(7(x1:S)) -> 7#(5(x1:S)) 213.26/216.93 9#(x1:S) -> 6#(7(x1:S)) 213.26/216.93 9#(x1:S) -> 7#(x1:S) 213.26/216.93 -> Rules: 213.26/216.93 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.93 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.93 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.93 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.93 2(8(x1:S)) -> 4(x1:S) 213.26/216.93 2(8(x1:S)) -> 7(x1:S) 213.26/216.93 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.93 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.93 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.93 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.93 5(9(x1:S)) -> 0(x1:S) 213.26/216.93 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.93 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.93 6(6(x1:S)) -> 3(x1:S) 213.26/216.93 6(9(x1:S)) -> 9(x1:S) 213.26/216.93 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.93 7(2(x1:S)) -> 4(x1:S) 213.26/216.93 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.93 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.93 9(x1:S) -> 6(7(x1:S)) 213.26/216.93 -> Usable rules: 213.26/216.93 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.93 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.93 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.93 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.93 2(8(x1:S)) -> 4(x1:S) 213.26/216.93 2(8(x1:S)) -> 7(x1:S) 213.26/216.93 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.93 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.93 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.93 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.93 5(9(x1:S)) -> 0(x1:S) 213.26/216.93 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.93 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.93 6(6(x1:S)) -> 3(x1:S) 213.26/216.93 6(9(x1:S)) -> 9(x1:S) 213.26/216.93 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.93 7(2(x1:S)) -> 4(x1:S) 213.26/216.93 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.93 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.93 9(x1:S) -> 6(7(x1:S)) 213.26/216.93 ->Interpretation type: 213.26/216.93 Linear 213.26/216.93 ->Coefficients: 213.26/216.93 Natural Numbers 213.26/216.93 ->Dimension: 213.26/216.93 1 213.26/216.93 ->Bound: 213.26/216.93 2 213.26/216.93 ->Interpretation: 213.26/216.93 213.26/216.93 [0](X) = 1 213.26/216.93 [2](X) = 2 213.26/216.93 [4](X) = 1 213.26/216.93 [5](X) = 1 213.26/216.93 [6](X) = 1 213.26/216.93 [7](X) = 1 213.26/216.93 [9](X) = 1 213.26/216.93 [1](X) = 1 213.26/216.93 [3](X) = 1 213.26/216.93 [8](X) = 0 213.26/216.93 [4#](X) = 2 213.26/216.93 [5#](X) = 2 213.26/216.93 [6#](X) = X 213.26/216.93 [7#](X) = 2 213.26/216.93 [9#](X) = 2 213.26/216.93 213.26/216.93 Problem 1.2: 213.26/216.93 213.26/216.93 SCC Processor: 213.26/216.93 -> Pairs: 213.26/216.93 4#(x1:S) -> 9#(6(6(x1:S))) 213.26/216.93 5#(2(6(x1:S))) -> 4#(x1:S) 213.26/216.93 5#(2(6(x1:S))) -> 6#(2(4(x1:S))) 213.26/216.93 6#(2(x1:S)) -> 7#(7(x1:S)) 213.26/216.93 6#(2(x1:S)) -> 7#(x1:S) 213.26/216.93 7#(0(x1:S)) -> 9#(3(x1:S)) 213.26/216.93 7#(2(x1:S)) -> 4#(x1:S) 213.26/216.93 9#(5(9(x1:S))) -> 5#(7(x1:S)) 213.26/216.93 9#(5(9(x1:S))) -> 7#(x1:S) 213.26/216.93 9#(7(x1:S)) -> 5#(x1:S) 213.26/216.93 9#(7(x1:S)) -> 7#(5(x1:S)) 213.26/216.93 9#(x1:S) -> 7#(x1:S) 213.26/216.93 -> Rules: 213.26/216.93 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.93 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.93 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.93 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.93 2(8(x1:S)) -> 4(x1:S) 213.26/216.93 2(8(x1:S)) -> 7(x1:S) 213.26/216.93 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.93 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.93 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.93 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.93 5(9(x1:S)) -> 0(x1:S) 213.26/216.93 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.93 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.93 6(6(x1:S)) -> 3(x1:S) 213.26/216.93 6(9(x1:S)) -> 9(x1:S) 213.26/216.93 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.93 7(2(x1:S)) -> 4(x1:S) 213.26/216.93 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.93 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.93 9(x1:S) -> 6(7(x1:S)) 213.26/216.93 ->Strongly Connected Components: 213.26/216.93 ->->Cycle: 213.26/216.93 ->->-> Pairs: 213.26/216.93 4#(x1:S) -> 9#(6(6(x1:S))) 213.26/216.93 5#(2(6(x1:S))) -> 4#(x1:S) 213.26/216.93 5#(2(6(x1:S))) -> 6#(2(4(x1:S))) 213.26/216.93 6#(2(x1:S)) -> 7#(7(x1:S)) 213.26/216.93 6#(2(x1:S)) -> 7#(x1:S) 213.26/216.93 7#(0(x1:S)) -> 9#(3(x1:S)) 213.26/216.93 7#(2(x1:S)) -> 4#(x1:S) 213.26/216.93 9#(5(9(x1:S))) -> 5#(7(x1:S)) 213.26/216.93 9#(5(9(x1:S))) -> 7#(x1:S) 213.26/216.93 9#(7(x1:S)) -> 5#(x1:S) 213.26/216.93 9#(7(x1:S)) -> 7#(5(x1:S)) 213.26/216.93 9#(x1:S) -> 7#(x1:S) 213.26/216.93 ->->-> Rules: 213.26/216.93 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.93 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.93 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.93 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.93 2(8(x1:S)) -> 4(x1:S) 213.26/216.93 2(8(x1:S)) -> 7(x1:S) 213.26/216.93 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.93 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.93 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.93 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.93 5(9(x1:S)) -> 0(x1:S) 213.26/216.93 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.93 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.93 6(6(x1:S)) -> 3(x1:S) 213.26/216.93 6(9(x1:S)) -> 9(x1:S) 213.26/216.93 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.93 7(2(x1:S)) -> 4(x1:S) 213.26/216.93 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.93 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.93 9(x1:S) -> 6(7(x1:S)) 213.26/216.93 213.26/216.93 Problem 1.2: 213.26/216.93 213.26/216.93 Reduction Pair Processor: 213.26/216.93 -> Pairs: 213.26/216.93 4#(x1:S) -> 9#(6(6(x1:S))) 213.26/216.93 5#(2(6(x1:S))) -> 4#(x1:S) 213.26/216.93 5#(2(6(x1:S))) -> 6#(2(4(x1:S))) 213.26/216.93 6#(2(x1:S)) -> 7#(7(x1:S)) 213.26/216.93 6#(2(x1:S)) -> 7#(x1:S) 213.26/216.93 7#(0(x1:S)) -> 9#(3(x1:S)) 213.26/216.93 7#(2(x1:S)) -> 4#(x1:S) 213.26/216.93 9#(5(9(x1:S))) -> 5#(7(x1:S)) 213.26/216.93 9#(5(9(x1:S))) -> 7#(x1:S) 213.26/216.93 9#(7(x1:S)) -> 5#(x1:S) 213.26/216.93 9#(7(x1:S)) -> 7#(5(x1:S)) 213.26/216.93 9#(x1:S) -> 7#(x1:S) 213.26/216.93 -> Rules: 213.26/216.93 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.93 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.93 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.93 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.93 2(8(x1:S)) -> 4(x1:S) 213.26/216.93 2(8(x1:S)) -> 7(x1:S) 213.26/216.93 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.93 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.93 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.93 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.93 5(9(x1:S)) -> 0(x1:S) 213.26/216.93 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.93 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.93 6(6(x1:S)) -> 3(x1:S) 213.26/216.93 6(9(x1:S)) -> 9(x1:S) 213.26/216.93 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.93 7(2(x1:S)) -> 4(x1:S) 213.26/216.93 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.93 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.93 9(x1:S) -> 6(7(x1:S)) 213.26/216.93 -> Usable rules: 213.26/216.93 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.93 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.93 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.93 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.93 2(8(x1:S)) -> 4(x1:S) 213.26/216.93 2(8(x1:S)) -> 7(x1:S) 213.26/216.93 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.93 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.93 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.93 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.93 5(9(x1:S)) -> 0(x1:S) 213.26/216.93 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.93 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.93 6(6(x1:S)) -> 3(x1:S) 213.26/216.93 6(9(x1:S)) -> 9(x1:S) 213.26/216.93 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.93 7(2(x1:S)) -> 4(x1:S) 213.26/216.93 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.93 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.93 9(x1:S) -> 6(7(x1:S)) 213.26/216.93 ->Interpretation type: 213.26/216.93 Linear 213.26/216.93 ->Coefficients: 213.26/216.93 Natural Numbers 213.26/216.93 ->Dimension: 213.26/216.93 2 213.26/216.93 ->Bound: 213.26/216.93 1 213.26/216.93 ->Interpretation: 213.26/216.93 213.26/216.93 [0](X) = [0;1] 213.26/216.93 [2](X) = [1 1;0 1].X + [1;0] 213.26/216.93 [4](X) = [1 0;0 0].X + [1;1] 213.26/216.93 [5](X) = [1 1;0 0].X + [0;1] 213.26/216.93 [6](X) = [1 0;0 0].X + [0;1] 213.26/216.93 [7](X) = [1 1;0 0].X + [0;1] 213.26/216.93 [9](X) = [1 1;0 0].X + [0;1] 213.26/216.93 [1](X) = [1 1;0 0].X + [1;1] 213.26/216.93 [3](X) = 0 213.26/216.93 [8](X) = [0 1;1 0].X + [0;1] 213.26/216.93 [4#](X) = [1 0;1 0].X + [1;1] 213.26/216.93 [5#](X) = [1 1;1 1].X + [0;1] 213.26/216.93 [6#](X) = [1 0;1 1].X 213.26/216.93 [7#](X) = [1 0;1 0].X + [0;1] 213.26/216.93 [9#](X) = [1 0;1 0].X + [0;1] 213.26/216.93 213.26/216.93 Problem 1.2: 213.26/216.93 213.26/216.93 SCC Processor: 213.26/216.93 -> Pairs: 213.26/216.93 5#(2(6(x1:S))) -> 4#(x1:S) 213.26/216.93 5#(2(6(x1:S))) -> 6#(2(4(x1:S))) 213.26/216.93 6#(2(x1:S)) -> 7#(7(x1:S)) 213.26/216.93 6#(2(x1:S)) -> 7#(x1:S) 213.26/216.93 7#(0(x1:S)) -> 9#(3(x1:S)) 213.26/216.93 7#(2(x1:S)) -> 4#(x1:S) 213.26/216.93 9#(5(9(x1:S))) -> 5#(7(x1:S)) 213.26/216.93 9#(5(9(x1:S))) -> 7#(x1:S) 213.26/216.93 9#(7(x1:S)) -> 5#(x1:S) 213.26/216.93 9#(7(x1:S)) -> 7#(5(x1:S)) 213.26/216.93 9#(x1:S) -> 7#(x1:S) 213.26/216.93 -> Rules: 213.26/216.93 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.93 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.93 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.93 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.93 2(8(x1:S)) -> 4(x1:S) 213.26/216.93 2(8(x1:S)) -> 7(x1:S) 213.26/216.93 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.93 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.93 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.93 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.93 5(9(x1:S)) -> 0(x1:S) 213.26/216.93 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.93 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.93 6(6(x1:S)) -> 3(x1:S) 213.26/216.93 6(9(x1:S)) -> 9(x1:S) 213.26/216.93 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.93 7(2(x1:S)) -> 4(x1:S) 213.26/216.93 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.93 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.93 9(x1:S) -> 6(7(x1:S)) 213.26/216.93 ->Strongly Connected Components: 213.26/216.93 ->->Cycle: 213.26/216.93 ->->-> Pairs: 213.26/216.93 7#(0(x1:S)) -> 9#(3(x1:S)) 213.26/216.93 9#(x1:S) -> 7#(x1:S) 213.26/216.93 ->->-> Rules: 213.26/216.93 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.93 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.93 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.93 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.93 2(8(x1:S)) -> 4(x1:S) 213.26/216.93 2(8(x1:S)) -> 7(x1:S) 213.26/216.93 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.93 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.93 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.93 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.93 5(9(x1:S)) -> 0(x1:S) 213.26/216.93 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.93 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.93 6(6(x1:S)) -> 3(x1:S) 213.26/216.93 6(9(x1:S)) -> 9(x1:S) 213.26/216.93 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.93 7(2(x1:S)) -> 4(x1:S) 213.26/216.93 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.93 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.93 9(x1:S) -> 6(7(x1:S)) 213.26/216.93 213.26/216.93 Problem 1.2: 213.26/216.93 213.26/216.93 Reduction Pair Processor: 213.26/216.93 -> Pairs: 213.26/216.93 7#(0(x1:S)) -> 9#(3(x1:S)) 213.26/216.93 9#(x1:S) -> 7#(x1:S) 213.26/216.93 -> Rules: 213.26/216.93 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.93 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.93 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.93 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.93 2(8(x1:S)) -> 4(x1:S) 213.26/216.93 2(8(x1:S)) -> 7(x1:S) 213.26/216.93 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.93 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.93 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.93 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.93 5(9(x1:S)) -> 0(x1:S) 213.26/216.93 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.93 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.93 6(6(x1:S)) -> 3(x1:S) 213.26/216.93 6(9(x1:S)) -> 9(x1:S) 213.26/216.93 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.93 7(2(x1:S)) -> 4(x1:S) 213.26/216.93 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.93 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.93 9(x1:S) -> 6(7(x1:S)) 213.26/216.93 -> Usable rules: 213.26/216.93 Empty 213.26/216.93 ->Interpretation type: 213.26/216.93 Linear 213.26/216.93 ->Coefficients: 213.26/216.93 Natural Numbers 213.26/216.93 ->Dimension: 213.26/216.93 1 213.26/216.93 ->Bound: 213.26/216.93 2 213.26/216.93 ->Interpretation: 213.26/216.93 213.26/216.93 [0](X) = 2.X + 2 213.26/216.93 [3](X) = 2.X + 1 213.26/216.93 [7#](X) = 2.X + 2 213.26/216.93 [9#](X) = 2.X + 2 213.26/216.93 213.26/216.93 Problem 1.2: 213.26/216.93 213.26/216.93 SCC Processor: 213.26/216.93 -> Pairs: 213.26/216.93 9#(x1:S) -> 7#(x1:S) 213.26/216.93 -> Rules: 213.26/216.93 0(3(x1:S)) -> 5(3(x1:S)) 213.26/216.93 2(4(x1:S)) -> 0(7(x1:S)) 213.26/216.93 2(7(x1:S)) -> 1(8(x1:S)) 213.26/216.93 2(8(1(x1:S))) -> 8(x1:S) 213.26/216.93 2(8(x1:S)) -> 4(x1:S) 213.26/216.93 2(8(x1:S)) -> 7(x1:S) 213.26/216.93 4(7(x1:S)) -> 1(3(x1:S)) 213.26/216.93 4(x1:S) -> 5(2(3(x1:S))) 213.26/216.93 4(x1:S) -> 9(6(6(x1:S))) 213.26/216.93 5(2(6(x1:S))) -> 6(2(4(x1:S))) 213.26/216.93 5(9(x1:S)) -> 0(x1:S) 213.26/216.93 5(3(x1:S)) -> 6(0(x1:S)) 213.26/216.93 6(2(x1:S)) -> 7(7(x1:S)) 213.26/216.93 6(6(x1:S)) -> 3(x1:S) 213.26/216.93 6(9(x1:S)) -> 9(x1:S) 213.26/216.93 7(0(x1:S)) -> 9(3(x1:S)) 213.26/216.93 7(2(x1:S)) -> 4(x1:S) 213.26/216.93 9(5(9(x1:S))) -> 5(7(x1:S)) 213.26/216.93 9(7(x1:S)) -> 7(5(x1:S)) 213.26/216.93 9(x1:S) -> 6(7(x1:S)) 213.26/216.93 ->Strongly Connected Components: 213.26/216.93 There is no strongly connected component 213.26/216.93 213.26/216.93 The problem is finite. 213.26/216.93 EOF