YES Problem: a12(a12(x1)) -> x1 a13(a13(x1)) -> x1 a14(a14(x1)) -> x1 a15(a15(x1)) -> x1 a16(a16(x1)) -> x1 a23(a23(x1)) -> x1 a24(a24(x1)) -> x1 a25(a25(x1)) -> x1 a26(a26(x1)) -> x1 a34(a34(x1)) -> x1 a35(a35(x1)) -> x1 a36(a36(x1)) -> x1 a45(a45(x1)) -> x1 a46(a46(x1)) -> x1 a56(a56(x1)) -> x1 a13(x1) -> a12(a23(a12(x1))) a14(x1) -> a12(a23(a34(a23(a12(x1))))) a15(x1) -> a12(a23(a34(a45(a34(a23(a12(x1))))))) a16(x1) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1))))))))) a24(x1) -> a23(a34(a23(x1))) a25(x1) -> a23(a34(a45(a34(a23(x1))))) a26(x1) -> a23(a34(a45(a56(a45(a34(a23(x1))))))) a35(x1) -> a34(a45(a34(x1))) a36(x1) -> a34(a45(a56(a45(a34(x1))))) a46(x1) -> a45(a56(a45(x1))) a12(a23(a12(a23(a12(a23(x1)))))) -> x1 a23(a34(a23(a34(a23(a34(x1)))))) -> x1 a34(a45(a34(a45(a34(a45(x1)))))) -> x1 a45(a56(a45(a56(a45(a56(x1)))))) -> x1 a12(a34(x1)) -> a34(a12(x1)) a12(a45(x1)) -> a45(a12(x1)) a12(a56(x1)) -> a56(a12(x1)) a23(a45(x1)) -> a45(a23(x1)) a23(a56(x1)) -> a56(a23(x1)) a34(a56(x1)) -> a56(a34(x1)) Proof: Arctic Interpretation Processor: dimension: 1 interpretation: [a56](x0) = x0, [a46](x0) = 8x0, [a45](x0) = 4x0, [a36](x0) = 8x0, [a35](x0) = 4x0, [a34](x0) = x0, [a26](x0) = 8x0, [a25](x0) = 10x0, [a24](x0) = 8x0, [a23](x0) = x0, [a16](x0) = 8x0, [a15](x0) = 9x0, [a14](x0) = x0, [a13](x0) = x0, [a12](x0) = x0 orientation: a12(a12(x1)) = x1 >= x1 = x1 a13(a13(x1)) = x1 >= x1 = x1 a14(a14(x1)) = x1 >= x1 = x1 a15(a15(x1)) = 18x1 >= x1 = x1 a16(a16(x1)) = 16x1 >= x1 = x1 a23(a23(x1)) = x1 >= x1 = x1 a24(a24(x1)) = 16x1 >= x1 = x1 a25(a25(x1)) = 20x1 >= x1 = x1 a26(a26(x1)) = 16x1 >= x1 = x1 a34(a34(x1)) = x1 >= x1 = x1 a35(a35(x1)) = 8x1 >= x1 = x1 a36(a36(x1)) = 16x1 >= x1 = x1 a45(a45(x1)) = 8x1 >= x1 = x1 a46(a46(x1)) = 16x1 >= x1 = x1 a56(a56(x1)) = x1 >= x1 = x1 a13(x1) = x1 >= x1 = a12(a23(a12(x1))) a14(x1) = x1 >= x1 = a12(a23(a34(a23(a12(x1))))) a15(x1) = 9x1 >= 4x1 = a12(a23(a34(a45(a34(a23(a12(x1))))))) a16(x1) = 8x1 >= 8x1 = a12(a23(a34(a45(a56(a45(a34(a23(a12(x1))))))))) a24(x1) = 8x1 >= x1 = a23(a34(a23(x1))) a25(x1) = 10x1 >= 4x1 = a23(a34(a45(a34(a23(x1))))) a26(x1) = 8x1 >= 8x1 = a23(a34(a45(a56(a45(a34(a23(x1))))))) a35(x1) = 4x1 >= 4x1 = a34(a45(a34(x1))) a36(x1) = 8x1 >= 8x1 = a34(a45(a56(a45(a34(x1))))) a46(x1) = 8x1 >= 8x1 = a45(a56(a45(x1))) a12(a23(a12(a23(a12(a23(x1)))))) = x1 >= x1 = x1 a23(a34(a23(a34(a23(a34(x1)))))) = x1 >= x1 = x1 a34(a45(a34(a45(a34(a45(x1)))))) = 12x1 >= x1 = x1 a45(a56(a45(a56(a45(a56(x1)))))) = 12x1 >= x1 = x1 a12(a34(x1)) = x1 >= x1 = a34(a12(x1)) a12(a45(x1)) = 4x1 >= 4x1 = a45(a12(x1)) a12(a56(x1)) = x1 >= x1 = a56(a12(x1)) a23(a45(x1)) = 4x1 >= 4x1 = a45(a23(x1)) a23(a56(x1)) = x1 >= x1 = a56(a23(x1)) a34(a56(x1)) = x1 >= x1 = a56(a34(x1)) problem: a12(a12(x1)) -> x1 a13(a13(x1)) -> x1 a14(a14(x1)) -> x1 a23(a23(x1)) -> x1 a34(a34(x1)) -> x1 a56(a56(x1)) -> x1 a13(x1) -> a12(a23(a12(x1))) a14(x1) -> a12(a23(a34(a23(a12(x1))))) a16(x1) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1))))))))) a26(x1) -> a23(a34(a45(a56(a45(a34(a23(x1))))))) a35(x1) -> a34(a45(a34(x1))) a36(x1) -> a34(a45(a56(a45(a34(x1))))) a46(x1) -> a45(a56(a45(x1))) a12(a23(a12(a23(a12(a23(x1)))))) -> x1 a23(a34(a23(a34(a23(a34(x1)))))) -> x1 a12(a34(x1)) -> a34(a12(x1)) a12(a45(x1)) -> a45(a12(x1)) a12(a56(x1)) -> a56(a12(x1)) a23(a45(x1)) -> a45(a23(x1)) a23(a56(x1)) -> a56(a23(x1)) a34(a56(x1)) -> a56(a34(x1)) Arctic Interpretation Processor: dimension: 1 interpretation: [a56](x0) = x0, [a46](x0) = 6x0, [a45](x0) = x0, [a36](x0) = 14x0, [a35](x0) = 14x0, [a34](x0) = 7x0, [a26](x0) = 14x0, [a23](x0) = x0, [a16](x0) = 14x0, [a14](x0) = 7x0, [a13](x0) = x0, [a12](x0) = x0 orientation: a12(a12(x1)) = x1 >= x1 = x1 a13(a13(x1)) = x1 >= x1 = x1 a14(a14(x1)) = 14x1 >= x1 = x1 a23(a23(x1)) = x1 >= x1 = x1 a34(a34(x1)) = 14x1 >= x1 = x1 a56(a56(x1)) = x1 >= x1 = x1 a13(x1) = x1 >= x1 = a12(a23(a12(x1))) a14(x1) = 7x1 >= 7x1 = a12(a23(a34(a23(a12(x1))))) a16(x1) = 14x1 >= 14x1 = a12(a23(a34(a45(a56(a45(a34(a23(a12(x1))))))))) a26(x1) = 14x1 >= 14x1 = a23(a34(a45(a56(a45(a34(a23(x1))))))) a35(x1) = 14x1 >= 14x1 = a34(a45(a34(x1))) a36(x1) = 14x1 >= 14x1 = a34(a45(a56(a45(a34(x1))))) a46(x1) = 6x1 >= x1 = a45(a56(a45(x1))) a12(a23(a12(a23(a12(a23(x1)))))) = x1 >= x1 = x1 a23(a34(a23(a34(a23(a34(x1)))))) = 21x1 >= x1 = x1 a12(a34(x1)) = 7x1 >= 7x1 = a34(a12(x1)) a12(a45(x1)) = x1 >= x1 = a45(a12(x1)) a12(a56(x1)) = x1 >= x1 = a56(a12(x1)) a23(a45(x1)) = x1 >= x1 = a45(a23(x1)) a23(a56(x1)) = x1 >= x1 = a56(a23(x1)) a34(a56(x1)) = 7x1 >= 7x1 = a56(a34(x1)) problem: a12(a12(x1)) -> x1 a13(a13(x1)) -> x1 a23(a23(x1)) -> x1 a56(a56(x1)) -> x1 a13(x1) -> a12(a23(a12(x1))) a14(x1) -> a12(a23(a34(a23(a12(x1))))) a16(x1) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1))))))))) a26(x1) -> a23(a34(a45(a56(a45(a34(a23(x1))))))) a35(x1) -> a34(a45(a34(x1))) a36(x1) -> a34(a45(a56(a45(a34(x1))))) a12(a23(a12(a23(a12(a23(x1)))))) -> x1 a12(a34(x1)) -> a34(a12(x1)) a12(a45(x1)) -> a45(a12(x1)) a12(a56(x1)) -> a56(a12(x1)) a23(a45(x1)) -> a45(a23(x1)) a23(a56(x1)) -> a56(a23(x1)) a34(a56(x1)) -> a56(a34(x1)) Arctic Interpretation Processor: dimension: 1 interpretation: [a56](x0) = 1x0, [a45](x0) = 5x0, [a36](x0) = 11x0, [a35](x0) = 5x0, [a34](x0) = x0, [a26](x0) = 11x0, [a23](x0) = x0, [a16](x0) = 11x0, [a14](x0) = x0, [a13](x0) = x0, [a12](x0) = x0 orientation: a12(a12(x1)) = x1 >= x1 = x1 a13(a13(x1)) = x1 >= x1 = x1 a23(a23(x1)) = x1 >= x1 = x1 a56(a56(x1)) = 2x1 >= x1 = x1 a13(x1) = x1 >= x1 = a12(a23(a12(x1))) a14(x1) = x1 >= x1 = a12(a23(a34(a23(a12(x1))))) a16(x1) = 11x1 >= 11x1 = a12(a23(a34(a45(a56(a45(a34(a23(a12(x1))))))))) a26(x1) = 11x1 >= 11x1 = a23(a34(a45(a56(a45(a34(a23(x1))))))) a35(x1) = 5x1 >= 5x1 = a34(a45(a34(x1))) a36(x1) = 11x1 >= 11x1 = a34(a45(a56(a45(a34(x1))))) a12(a23(a12(a23(a12(a23(x1)))))) = x1 >= x1 = x1 a12(a34(x1)) = x1 >= x1 = a34(a12(x1)) a12(a45(x1)) = 5x1 >= 5x1 = a45(a12(x1)) a12(a56(x1)) = 1x1 >= 1x1 = a56(a12(x1)) a23(a45(x1)) = 5x1 >= 5x1 = a45(a23(x1)) a23(a56(x1)) = 1x1 >= 1x1 = a56(a23(x1)) a34(a56(x1)) = 1x1 >= 1x1 = a56(a34(x1)) problem: a12(a12(x1)) -> x1 a13(a13(x1)) -> x1 a23(a23(x1)) -> x1 a13(x1) -> a12(a23(a12(x1))) a14(x1) -> a12(a23(a34(a23(a12(x1))))) a16(x1) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1))))))))) a26(x1) -> a23(a34(a45(a56(a45(a34(a23(x1))))))) a35(x1) -> a34(a45(a34(x1))) a36(x1) -> a34(a45(a56(a45(a34(x1))))) a12(a23(a12(a23(a12(a23(x1)))))) -> x1 a12(a34(x1)) -> a34(a12(x1)) a12(a45(x1)) -> a45(a12(x1)) a12(a56(x1)) -> a56(a12(x1)) a23(a45(x1)) -> a45(a23(x1)) a23(a56(x1)) -> a56(a23(x1)) a34(a56(x1)) -> a56(a34(x1)) Arctic Interpretation Processor: dimension: 1 interpretation: [a56](x0) = 1x0, [a45](x0) = x0, [a36](x0) = 1x0, [a35](x0) = x0, [a34](x0) = x0, [a26](x0) = 3x0, [a23](x0) = 1x0, [a16](x0) = 3x0, [a14](x0) = 2x0, [a13](x0) = 1x0, [a12](x0) = x0 orientation: a12(a12(x1)) = x1 >= x1 = x1 a13(a13(x1)) = 2x1 >= x1 = x1 a23(a23(x1)) = 2x1 >= x1 = x1 a13(x1) = 1x1 >= 1x1 = a12(a23(a12(x1))) a14(x1) = 2x1 >= 2x1 = a12(a23(a34(a23(a12(x1))))) a16(x1) = 3x1 >= 3x1 = a12(a23(a34(a45(a56(a45(a34(a23(a12(x1))))))))) a26(x1) = 3x1 >= 3x1 = a23(a34(a45(a56(a45(a34(a23(x1))))))) a35(x1) = x1 >= x1 = a34(a45(a34(x1))) a36(x1) = 1x1 >= 1x1 = a34(a45(a56(a45(a34(x1))))) a12(a23(a12(a23(a12(a23(x1)))))) = 3x1 >= x1 = x1 a12(a34(x1)) = x1 >= x1 = a34(a12(x1)) a12(a45(x1)) = x1 >= x1 = a45(a12(x1)) a12(a56(x1)) = 1x1 >= 1x1 = a56(a12(x1)) a23(a45(x1)) = 1x1 >= 1x1 = a45(a23(x1)) a23(a56(x1)) = 2x1 >= 2x1 = a56(a23(x1)) a34(a56(x1)) = 1x1 >= 1x1 = a56(a34(x1)) problem: a12(a12(x1)) -> x1 a13(x1) -> a12(a23(a12(x1))) a14(x1) -> a12(a23(a34(a23(a12(x1))))) a16(x1) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1))))))))) a26(x1) -> a23(a34(a45(a56(a45(a34(a23(x1))))))) a35(x1) -> a34(a45(a34(x1))) a36(x1) -> a34(a45(a56(a45(a34(x1))))) a12(a34(x1)) -> a34(a12(x1)) a12(a45(x1)) -> a45(a12(x1)) a12(a56(x1)) -> a56(a12(x1)) a23(a45(x1)) -> a45(a23(x1)) a23(a56(x1)) -> a56(a23(x1)) a34(a56(x1)) -> a56(a34(x1)) Arctic Interpretation Processor: dimension: 1 interpretation: [a56](x0) = 2x0, [a45](x0) = x0, [a36](x0) = 4x0, [a35](x0) = 2x0, [a34](x0) = 1x0, [a26](x0) = 8x0, [a23](x0) = x0, [a16](x0) = 6x0, [a14](x0) = 3x0, [a13](x0) = 2x0, [a12](x0) = 1x0 orientation: a12(a12(x1)) = 2x1 >= x1 = x1 a13(x1) = 2x1 >= 2x1 = a12(a23(a12(x1))) a14(x1) = 3x1 >= 3x1 = a12(a23(a34(a23(a12(x1))))) a16(x1) = 6x1 >= 6x1 = a12(a23(a34(a45(a56(a45(a34(a23(a12(x1))))))))) a26(x1) = 8x1 >= 4x1 = a23(a34(a45(a56(a45(a34(a23(x1))))))) a35(x1) = 2x1 >= 2x1 = a34(a45(a34(x1))) a36(x1) = 4x1 >= 4x1 = a34(a45(a56(a45(a34(x1))))) a12(a34(x1)) = 2x1 >= 2x1 = a34(a12(x1)) a12(a45(x1)) = 1x1 >= 1x1 = a45(a12(x1)) a12(a56(x1)) = 3x1 >= 3x1 = a56(a12(x1)) a23(a45(x1)) = x1 >= x1 = a45(a23(x1)) a23(a56(x1)) = 2x1 >= 2x1 = a56(a23(x1)) a34(a56(x1)) = 3x1 >= 3x1 = a56(a34(x1)) problem: a13(x1) -> a12(a23(a12(x1))) a14(x1) -> a12(a23(a34(a23(a12(x1))))) a16(x1) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1))))))))) a35(x1) -> a34(a45(a34(x1))) a36(x1) -> a34(a45(a56(a45(a34(x1))))) a12(a34(x1)) -> a34(a12(x1)) a12(a45(x1)) -> a45(a12(x1)) a12(a56(x1)) -> a56(a12(x1)) a23(a45(x1)) -> a45(a23(x1)) a23(a56(x1)) -> a56(a23(x1)) a34(a56(x1)) -> a56(a34(x1)) Arctic Interpretation Processor: dimension: 1 interpretation: [a56](x0) = 4x0, [a45](x0) = x0, [a36](x0) = 8x0, [a35](x0) = x0, [a34](x0) = x0, [a23](x0) = x0, [a16](x0) = 4x0, [a14](x0) = x0, [a13](x0) = x0, [a12](x0) = x0 orientation: a13(x1) = x1 >= x1 = a12(a23(a12(x1))) a14(x1) = x1 >= x1 = a12(a23(a34(a23(a12(x1))))) a16(x1) = 4x1 >= 4x1 = a12(a23(a34(a45(a56(a45(a34(a23(a12(x1))))))))) a35(x1) = x1 >= x1 = a34(a45(a34(x1))) a36(x1) = 8x1 >= 4x1 = a34(a45(a56(a45(a34(x1))))) a12(a34(x1)) = x1 >= x1 = a34(a12(x1)) a12(a45(x1)) = x1 >= x1 = a45(a12(x1)) a12(a56(x1)) = 4x1 >= 4x1 = a56(a12(x1)) a23(a45(x1)) = x1 >= x1 = a45(a23(x1)) a23(a56(x1)) = 4x1 >= 4x1 = a56(a23(x1)) a34(a56(x1)) = 4x1 >= 4x1 = a56(a34(x1)) problem: a13(x1) -> a12(a23(a12(x1))) a14(x1) -> a12(a23(a34(a23(a12(x1))))) a16(x1) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1))))))))) a35(x1) -> a34(a45(a34(x1))) a12(a34(x1)) -> a34(a12(x1)) a12(a45(x1)) -> a45(a12(x1)) a12(a56(x1)) -> a56(a12(x1)) a23(a45(x1)) -> a45(a23(x1)) a23(a56(x1)) -> a56(a23(x1)) a34(a56(x1)) -> a56(a34(x1)) Arctic Interpretation Processor: dimension: 1 interpretation: [a56](x0) = 2x0, [a45](x0) = 2x0, [a35](x0) = 4x0, [a34](x0) = 1x0, [a23](x0) = x0, [a16](x0) = 8x0, [a14](x0) = 2x0, [a13](x0) = 4x0, [a12](x0) = x0 orientation: a13(x1) = 4x1 >= x1 = a12(a23(a12(x1))) a14(x1) = 2x1 >= 1x1 = a12(a23(a34(a23(a12(x1))))) a16(x1) = 8x1 >= 8x1 = a12(a23(a34(a45(a56(a45(a34(a23(a12(x1))))))))) a35(x1) = 4x1 >= 4x1 = a34(a45(a34(x1))) a12(a34(x1)) = 1x1 >= 1x1 = a34(a12(x1)) a12(a45(x1)) = 2x1 >= 2x1 = a45(a12(x1)) a12(a56(x1)) = 2x1 >= 2x1 = a56(a12(x1)) a23(a45(x1)) = 2x1 >= 2x1 = a45(a23(x1)) a23(a56(x1)) = 2x1 >= 2x1 = a56(a23(x1)) a34(a56(x1)) = 3x1 >= 3x1 = a56(a34(x1)) problem: a16(x1) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1))))))))) a35(x1) -> a34(a45(a34(x1))) a12(a34(x1)) -> a34(a12(x1)) a12(a45(x1)) -> a45(a12(x1)) a12(a56(x1)) -> a56(a12(x1)) a23(a45(x1)) -> a45(a23(x1)) a23(a56(x1)) -> a56(a23(x1)) a34(a56(x1)) -> a56(a34(x1)) Arctic Interpretation Processor: dimension: 1 interpretation: [a56](x0) = 6x0, [a45](x0) = x0, [a35](x0) = 8x0, [a34](x0) = 1x0, [a23](x0) = x0, [a16](x0) = 14x0, [a12](x0) = 3x0 orientation: a16(x1) = 14x1 >= 14x1 = a12(a23(a34(a45(a56(a45(a34(a23(a12(x1))))))))) a35(x1) = 8x1 >= 2x1 = a34(a45(a34(x1))) a12(a34(x1)) = 4x1 >= 4x1 = a34(a12(x1)) a12(a45(x1)) = 3x1 >= 3x1 = a45(a12(x1)) a12(a56(x1)) = 9x1 >= 9x1 = a56(a12(x1)) a23(a45(x1)) = x1 >= x1 = a45(a23(x1)) a23(a56(x1)) = 6x1 >= 6x1 = a56(a23(x1)) a34(a56(x1)) = 7x1 >= 7x1 = a56(a34(x1)) problem: a16(x1) -> a12(a23(a34(a45(a56(a45(a34(a23(a12(x1))))))))) a12(a34(x1)) -> a34(a12(x1)) a12(a45(x1)) -> a45(a12(x1)) a12(a56(x1)) -> a56(a12(x1)) a23(a45(x1)) -> a45(a23(x1)) a23(a56(x1)) -> a56(a23(x1)) a34(a56(x1)) -> a56(a34(x1)) Arctic Interpretation Processor: dimension: 1 interpretation: [a56](x0) = 12x0, [a45](x0) = x0, [a34](x0) = x0, [a23](x0) = x0, [a16](x0) = 14x0, [a12](x0) = x0 orientation: a16(x1) = 14x1 >= 12x1 = a12(a23(a34(a45(a56(a45(a34(a23(a12(x1))))))))) a12(a34(x1)) = x1 >= x1 = a34(a12(x1)) a12(a45(x1)) = x1 >= x1 = a45(a12(x1)) a12(a56(x1)) = 12x1 >= 12x1 = a56(a12(x1)) a23(a45(x1)) = x1 >= x1 = a45(a23(x1)) a23(a56(x1)) = 12x1 >= 12x1 = a56(a23(x1)) a34(a56(x1)) = 12x1 >= 12x1 = a56(a34(x1)) problem: a12(a34(x1)) -> a34(a12(x1)) a12(a45(x1)) -> a45(a12(x1)) a12(a56(x1)) -> a56(a12(x1)) a23(a45(x1)) -> a45(a23(x1)) a23(a56(x1)) -> a56(a23(x1)) a34(a56(x1)) -> a56(a34(x1)) KBO Processor: weight function: w0 = 1 w(a56) = w(a45) = w(a34) = w(a23) = w(a12) = 1 precedence: a23 > a12 > a34 > a56 ~ a45 problem: Qed