/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: 1(1(x1)) -> 4(3(x1)) 1(2(x1)) -> 2(1(x1)) 2(2(x1)) -> 1(1(1(x1))) 3(3(x1)) -> 5(6(x1)) 3(4(x1)) -> 1(1(x1)) 4(4(x1)) -> 3(x1) 5(5(x1)) -> 6(2(x1)) 5(6(x1)) -> 1(2(x1)) 6(6(x1)) -> 2(1(x1)) Proof: String Reversal Processor: 1(1(x1)) -> 3(4(x1)) 2(1(x1)) -> 1(2(x1)) 2(2(x1)) -> 1(1(1(x1))) 3(3(x1)) -> 6(5(x1)) 4(3(x1)) -> 1(1(x1)) 4(4(x1)) -> 3(x1) 5(5(x1)) -> 2(6(x1)) 6(5(x1)) -> 2(1(x1)) 6(6(x1)) -> 1(2(x1)) DP Processor: DPs: 1#(1(x1)) -> 4#(x1) 1#(1(x1)) -> 3#(4(x1)) 2#(1(x1)) -> 2#(x1) 2#(1(x1)) -> 1#(2(x1)) 2#(2(x1)) -> 1#(x1) 2#(2(x1)) -> 1#(1(x1)) 2#(2(x1)) -> 1#(1(1(x1))) 3#(3(x1)) -> 5#(x1) 3#(3(x1)) -> 6#(5(x1)) 4#(3(x1)) -> 1#(x1) 4#(3(x1)) -> 1#(1(x1)) 4#(4(x1)) -> 3#(x1) 5#(5(x1)) -> 6#(x1) 5#(5(x1)) -> 2#(6(x1)) 6#(5(x1)) -> 1#(x1) 6#(5(x1)) -> 2#(1(x1)) 6#(6(x1)) -> 2#(x1) 6#(6(x1)) -> 1#(2(x1)) TRS: 1(1(x1)) -> 3(4(x1)) 2(1(x1)) -> 1(2(x1)) 2(2(x1)) -> 1(1(1(x1))) 3(3(x1)) -> 6(5(x1)) 4(3(x1)) -> 1(1(x1)) 4(4(x1)) -> 3(x1) 5(5(x1)) -> 2(6(x1)) 6(5(x1)) -> 2(1(x1)) 6(6(x1)) -> 1(2(x1)) TDG Processor: DPs: 1#(1(x1)) -> 4#(x1) 1#(1(x1)) -> 3#(4(x1)) 2#(1(x1)) -> 2#(x1) 2#(1(x1)) -> 1#(2(x1)) 2#(2(x1)) -> 1#(x1) 2#(2(x1)) -> 1#(1(x1)) 2#(2(x1)) -> 1#(1(1(x1))) 3#(3(x1)) -> 5#(x1) 3#(3(x1)) -> 6#(5(x1)) 4#(3(x1)) -> 1#(x1) 4#(3(x1)) -> 1#(1(x1)) 4#(4(x1)) -> 3#(x1) 5#(5(x1)) -> 6#(x1) 5#(5(x1)) -> 2#(6(x1)) 6#(5(x1)) -> 1#(x1) 6#(5(x1)) -> 2#(1(x1)) 6#(6(x1)) -> 2#(x1) 6#(6(x1)) -> 1#(2(x1)) TRS: 1(1(x1)) -> 3(4(x1)) 2(1(x1)) -> 1(2(x1)) 2(2(x1)) -> 1(1(1(x1))) 3(3(x1)) -> 6(5(x1)) 4(3(x1)) -> 1(1(x1)) 4(4(x1)) -> 3(x1) 5(5(x1)) -> 2(6(x1)) 6(5(x1)) -> 2(1(x1)) 6(6(x1)) -> 1(2(x1)) graph: 6#(5(x1)) -> 2#(1(x1)) -> 2#(2(x1)) -> 1#(1(1(x1))) 6#(5(x1)) -> 2#(1(x1)) -> 2#(2(x1)) -> 1#(1(x1)) 6#(5(x1)) -> 2#(1(x1)) -> 2#(2(x1)) -> 1#(x1) 6#(5(x1)) -> 2#(1(x1)) -> 2#(1(x1)) -> 1#(2(x1)) 6#(5(x1)) -> 2#(1(x1)) -> 2#(1(x1)) -> 2#(x1) 6#(5(x1)) -> 1#(x1) -> 1#(1(x1)) -> 3#(4(x1)) 6#(5(x1)) -> 1#(x1) -> 1#(1(x1)) -> 4#(x1) 6#(6(x1)) -> 2#(x1) -> 2#(2(x1)) -> 1#(1(1(x1))) 6#(6(x1)) -> 2#(x1) -> 2#(2(x1)) -> 1#(1(x1)) 6#(6(x1)) -> 2#(x1) -> 2#(2(x1)) -> 1#(x1) 6#(6(x1)) -> 2#(x1) -> 2#(1(x1)) -> 1#(2(x1)) 6#(6(x1)) -> 2#(x1) -> 2#(1(x1)) -> 2#(x1) 6#(6(x1)) -> 1#(2(x1)) -> 1#(1(x1)) -> 3#(4(x1)) 6#(6(x1)) -> 1#(2(x1)) -> 1#(1(x1)) -> 4#(x1) 5#(5(x1)) -> 6#(x1) -> 6#(6(x1)) -> 1#(2(x1)) 5#(5(x1)) -> 6#(x1) -> 6#(6(x1)) -> 2#(x1) 5#(5(x1)) -> 6#(x1) -> 6#(5(x1)) -> 2#(1(x1)) 5#(5(x1)) -> 6#(x1) -> 6#(5(x1)) -> 1#(x1) 5#(5(x1)) -> 2#(6(x1)) -> 2#(2(x1)) -> 1#(1(1(x1))) 5#(5(x1)) -> 2#(6(x1)) -> 2#(2(x1)) -> 1#(1(x1)) 5#(5(x1)) -> 2#(6(x1)) -> 2#(2(x1)) -> 1#(x1) 5#(5(x1)) -> 2#(6(x1)) -> 2#(1(x1)) -> 1#(2(x1)) 5#(5(x1)) -> 2#(6(x1)) -> 2#(1(x1)) -> 2#(x1) 2#(2(x1)) -> 1#(1(1(x1))) -> 1#(1(x1)) -> 3#(4(x1)) 2#(2(x1)) -> 1#(1(1(x1))) -> 1#(1(x1)) -> 4#(x1) 2#(2(x1)) -> 1#(1(x1)) -> 1#(1(x1)) -> 3#(4(x1)) 2#(2(x1)) -> 1#(1(x1)) -> 1#(1(x1)) -> 4#(x1) 2#(2(x1)) -> 1#(x1) -> 1#(1(x1)) -> 3#(4(x1)) 2#(2(x1)) -> 1#(x1) -> 1#(1(x1)) -> 4#(x1) 2#(1(x1)) -> 2#(x1) -> 2#(2(x1)) -> 1#(1(1(x1))) 2#(1(x1)) -> 2#(x1) -> 2#(2(x1)) -> 1#(1(x1)) 2#(1(x1)) -> 2#(x1) -> 2#(2(x1)) -> 1#(x1) 2#(1(x1)) -> 2#(x1) -> 2#(1(x1)) -> 1#(2(x1)) 2#(1(x1)) -> 2#(x1) -> 2#(1(x1)) -> 2#(x1) 2#(1(x1)) -> 1#(2(x1)) -> 1#(1(x1)) -> 3#(4(x1)) 2#(1(x1)) -> 1#(2(x1)) -> 1#(1(x1)) -> 4#(x1) 3#(3(x1)) -> 6#(5(x1)) -> 6#(6(x1)) -> 1#(2(x1)) 3#(3(x1)) -> 6#(5(x1)) -> 6#(6(x1)) -> 2#(x1) 3#(3(x1)) -> 6#(5(x1)) -> 6#(5(x1)) -> 2#(1(x1)) 3#(3(x1)) -> 6#(5(x1)) -> 6#(5(x1)) -> 1#(x1) 3#(3(x1)) -> 5#(x1) -> 5#(5(x1)) -> 2#(6(x1)) 3#(3(x1)) -> 5#(x1) -> 5#(5(x1)) -> 6#(x1) 4#(4(x1)) -> 3#(x1) -> 3#(3(x1)) -> 6#(5(x1)) 4#(4(x1)) -> 3#(x1) -> 3#(3(x1)) -> 5#(x1) 4#(3(x1)) -> 1#(1(x1)) -> 1#(1(x1)) -> 3#(4(x1)) 4#(3(x1)) -> 1#(1(x1)) -> 1#(1(x1)) -> 4#(x1) 4#(3(x1)) -> 1#(x1) -> 1#(1(x1)) -> 3#(4(x1)) 4#(3(x1)) -> 1#(x1) -> 1#(1(x1)) -> 4#(x1) 1#(1(x1)) -> 3#(4(x1)) -> 3#(3(x1)) -> 6#(5(x1)) 1#(1(x1)) -> 3#(4(x1)) -> 3#(3(x1)) -> 5#(x1) 1#(1(x1)) -> 4#(x1) -> 4#(4(x1)) -> 3#(x1) 1#(1(x1)) -> 4#(x1) -> 4#(3(x1)) -> 1#(1(x1)) 1#(1(x1)) -> 4#(x1) -> 4#(3(x1)) -> 1#(x1) Matrix Interpretation Processor: dim=1 interpretation: [6#](x0) = x0 + 9, [5#](x0) = x0 + 24, [2#](x0) = x0 + 15, [3#](x0) = x0 + 10, [4#](x0) = x0, [1#](x0) = x0 + 5, [5](x0) = x0 + 22, [6](x0) = x0 + 20, [2](x0) = x0 + 24, [4](x0) = x0 + 11, [3](x0) = x0 + 21, [1](x0) = x0 + 16 orientation: 1#(1(x1)) = x1 + 21 >= x1 = 4#(x1) 1#(1(x1)) = x1 + 21 >= x1 + 21 = 3#(4(x1)) 2#(1(x1)) = x1 + 31 >= x1 + 15 = 2#(x1) 2#(1(x1)) = x1 + 31 >= x1 + 29 = 1#(2(x1)) 2#(2(x1)) = x1 + 39 >= x1 + 5 = 1#(x1) 2#(2(x1)) = x1 + 39 >= x1 + 21 = 1#(1(x1)) 2#(2(x1)) = x1 + 39 >= x1 + 37 = 1#(1(1(x1))) 3#(3(x1)) = x1 + 31 >= x1 + 24 = 5#(x1) 3#(3(x1)) = x1 + 31 >= x1 + 31 = 6#(5(x1)) 4#(3(x1)) = x1 + 21 >= x1 + 5 = 1#(x1) 4#(3(x1)) = x1 + 21 >= x1 + 21 = 1#(1(x1)) 4#(4(x1)) = x1 + 11 >= x1 + 10 = 3#(x1) 5#(5(x1)) = x1 + 46 >= x1 + 9 = 6#(x1) 5#(5(x1)) = x1 + 46 >= x1 + 35 = 2#(6(x1)) 6#(5(x1)) = x1 + 31 >= x1 + 5 = 1#(x1) 6#(5(x1)) = x1 + 31 >= x1 + 31 = 2#(1(x1)) 6#(6(x1)) = x1 + 29 >= x1 + 15 = 2#(x1) 6#(6(x1)) = x1 + 29 >= x1 + 29 = 1#(2(x1)) 1(1(x1)) = x1 + 32 >= x1 + 32 = 3(4(x1)) 2(1(x1)) = x1 + 40 >= x1 + 40 = 1(2(x1)) 2(2(x1)) = x1 + 48 >= x1 + 48 = 1(1(1(x1))) 3(3(x1)) = x1 + 42 >= x1 + 42 = 6(5(x1)) 4(3(x1)) = x1 + 32 >= x1 + 32 = 1(1(x1)) 4(4(x1)) = x1 + 22 >= x1 + 21 = 3(x1) 5(5(x1)) = x1 + 44 >= x1 + 44 = 2(6(x1)) 6(5(x1)) = x1 + 42 >= x1 + 40 = 2(1(x1)) 6(6(x1)) = x1 + 40 >= x1 + 40 = 1(2(x1)) problem: DPs: 1#(1(x1)) -> 3#(4(x1)) 3#(3(x1)) -> 6#(5(x1)) 4#(3(x1)) -> 1#(1(x1)) 6#(5(x1)) -> 2#(1(x1)) 6#(6(x1)) -> 1#(2(x1)) TRS: 1(1(x1)) -> 3(4(x1)) 2(1(x1)) -> 1(2(x1)) 2(2(x1)) -> 1(1(1(x1))) 3(3(x1)) -> 6(5(x1)) 4(3(x1)) -> 1(1(x1)) 4(4(x1)) -> 3(x1) 5(5(x1)) -> 2(6(x1)) 6(5(x1)) -> 2(1(x1)) 6(6(x1)) -> 1(2(x1)) Restore Modifier: DPs: 1#(1(x1)) -> 3#(4(x1)) 3#(3(x1)) -> 6#(5(x1)) 4#(3(x1)) -> 1#(1(x1)) 6#(5(x1)) -> 2#(1(x1)) 6#(6(x1)) -> 1#(2(x1)) TRS: 1(1(x1)) -> 3(4(x1)) 2(1(x1)) -> 1(2(x1)) 2(2(x1)) -> 1(1(1(x1))) 3(3(x1)) -> 6(5(x1)) 4(3(x1)) -> 1(1(x1)) 4(4(x1)) -> 3(x1) 5(5(x1)) -> 2(6(x1)) 6(5(x1)) -> 2(1(x1)) 6(6(x1)) -> 1(2(x1)) EDG Processor: DPs: 1#(1(x1)) -> 3#(4(x1)) 3#(3(x1)) -> 6#(5(x1)) 4#(3(x1)) -> 1#(1(x1)) 6#(5(x1)) -> 2#(1(x1)) 6#(6(x1)) -> 1#(2(x1)) TRS: 1(1(x1)) -> 3(4(x1)) 2(1(x1)) -> 1(2(x1)) 2(2(x1)) -> 1(1(1(x1))) 3(3(x1)) -> 6(5(x1)) 4(3(x1)) -> 1(1(x1)) 4(4(x1)) -> 3(x1) 5(5(x1)) -> 2(6(x1)) 6(5(x1)) -> 2(1(x1)) 6(6(x1)) -> 1(2(x1)) graph: 6#(6(x1)) -> 1#(2(x1)) -> 1#(1(x1)) -> 3#(4(x1)) 3#(3(x1)) -> 6#(5(x1)) -> 6#(5(x1)) -> 2#(1(x1)) 3#(3(x1)) -> 6#(5(x1)) -> 6#(6(x1)) -> 1#(2(x1)) 4#(3(x1)) -> 1#(1(x1)) -> 1#(1(x1)) -> 3#(4(x1)) 1#(1(x1)) -> 3#(4(x1)) -> 3#(3(x1)) -> 6#(5(x1)) SCC Processor: #sccs: 1 #rules: 3 #arcs: 5/25 DPs: 6#(6(x1)) -> 1#(2(x1)) 1#(1(x1)) -> 3#(4(x1)) 3#(3(x1)) -> 6#(5(x1)) TRS: 1(1(x1)) -> 3(4(x1)) 2(1(x1)) -> 1(2(x1)) 2(2(x1)) -> 1(1(1(x1))) 3(3(x1)) -> 6(5(x1)) 4(3(x1)) -> 1(1(x1)) 4(4(x1)) -> 3(x1) 5(5(x1)) -> 2(6(x1)) 6(5(x1)) -> 2(1(x1)) 6(6(x1)) -> 1(2(x1)) Matrix Interpretation Processor: dim=4 interpretation: [6#](x0) = [1 0 1 0]x0, [3#](x0) = [0 0 1 0]x0, [1#](x0) = [0 0 0 1]x0 + [1], [0 0 0 0] [0] [0 1 0 0] [0] [5](x0) = [0 0 0 1]x0 + [0] [0 0 0 0] [1], [1 0 0 0] [0] [0 1 0 0] [0] [6](x0) = [0 0 0 0]x0 + [1] [0 0 0 0] [0], [0 0 0 0] [0] [0 1 0 0] [0] [2](x0) = [0 0 0 0]x0 + [1] [0 0 0 0] [0], [0 0 0 1] [0] [0 1 0 0] [0] [4](x0) = [1 0 0 0]x0 + [1] [0 0 0 0] [0], [0 0 0 0] [0] [0 1 0 0] [0] [3](x0) = [0 0 0 1]x0 + [1] [0 0 0 0] [0], [0 0 0 0] [0] [0 1 0 0] [0] [1](x0) = [0 0 0 0]x0 + [1] [1 0 0 0] [0] orientation: 6#(6(x1)) = [1 0 0 0]x1 + [1] >= [1] = 1#(2(x1)) 1#(1(x1)) = [1 0 0 0]x1 + [1] >= [1 0 0 0]x1 + [1] = 3#(4(x1)) 3#(3(x1)) = [0 0 0 1]x1 + [1] >= [0 0 0 1]x1 = 6#(5(x1)) [0 0 0 0] [0] [0 0 0 0] [0] [0 1 0 0] [0] [0 1 0 0] [0] 1(1(x1)) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = 3(4(x1)) [0 0 0 0] [0] [0 0 0 0] [0] [0 0 0 0] [0] [0 0 0 0] [0] [0 1 0 0] [0] [0 1 0 0] [0] 2(1(x1)) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = 1(2(x1)) [0 0 0 0] [0] [0 0 0 0] [0] [0 0 0 0] [0] [0 0 0 0] [0] [0 1 0 0] [0] [0 1 0 0] [0] 2(2(x1)) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = 1(1(1(x1))) [0 0 0 0] [0] [0 0 0 0] [0] [0 0 0 0] [0] [0 0 0 0] [0] [0 1 0 0] [0] [0 1 0 0] [0] 3(3(x1)) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = 6(5(x1)) [0 0 0 0] [0] [0 0 0 0] [0] [0 0 0 0] [0] [0 0 0 0] [0] [0 1 0 0] [0] [0 1 0 0] [0] 4(3(x1)) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = 1(1(x1)) [0 0 0 0] [0] [0 0 0 0] [0] [0 0 0 0] [0] [0 0 0 0] [0] [0 1 0 0] [0] [0 1 0 0] [0] 4(4(x1)) = [0 0 0 1]x1 + [1] >= [0 0 0 1]x1 + [1] = 3(x1) [0 0 0 0] [0] [0 0 0 0] [0] [0 0 0 0] [0] [0 0 0 0] [0] [0 1 0 0] [0] [0 1 0 0] [0] 5(5(x1)) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = 2(6(x1)) [0 0 0 0] [1] [0 0 0 0] [0] [0 0 0 0] [0] [0 0 0 0] [0] [0 1 0 0] [0] [0 1 0 0] [0] 6(5(x1)) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = 2(1(x1)) [0 0 0 0] [0] [0 0 0 0] [0] [1 0 0 0] [0] [0 0 0 0] [0] [0 1 0 0] [0] [0 1 0 0] [0] 6(6(x1)) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = 1(2(x1)) [0 0 0 0] [0] [0 0 0 0] [0] problem: DPs: 6#(6(x1)) -> 1#(2(x1)) 1#(1(x1)) -> 3#(4(x1)) TRS: 1(1(x1)) -> 3(4(x1)) 2(1(x1)) -> 1(2(x1)) 2(2(x1)) -> 1(1(1(x1))) 3(3(x1)) -> 6(5(x1)) 4(3(x1)) -> 1(1(x1)) 4(4(x1)) -> 3(x1) 5(5(x1)) -> 2(6(x1)) 6(5(x1)) -> 2(1(x1)) 6(6(x1)) -> 1(2(x1)) Restore Modifier: DPs: 6#(6(x1)) -> 1#(2(x1)) 1#(1(x1)) -> 3#(4(x1)) TRS: 1(1(x1)) -> 3(4(x1)) 2(1(x1)) -> 1(2(x1)) 2(2(x1)) -> 1(1(1(x1))) 3(3(x1)) -> 6(5(x1)) 4(3(x1)) -> 1(1(x1)) 4(4(x1)) -> 3(x1) 5(5(x1)) -> 2(6(x1)) 6(5(x1)) -> 2(1(x1)) 6(6(x1)) -> 1(2(x1)) EDG Processor: DPs: 6#(6(x1)) -> 1#(2(x1)) 1#(1(x1)) -> 3#(4(x1)) TRS: 1(1(x1)) -> 3(4(x1)) 2(1(x1)) -> 1(2(x1)) 2(2(x1)) -> 1(1(1(x1))) 3(3(x1)) -> 6(5(x1)) 4(3(x1)) -> 1(1(x1)) 4(4(x1)) -> 3(x1) 5(5(x1)) -> 2(6(x1)) 6(5(x1)) -> 2(1(x1)) 6(6(x1)) -> 1(2(x1)) graph: 6#(6(x1)) -> 1#(2(x1)) -> 1#(1(x1)) -> 3#(4(x1)) SCC Processor: #sccs: 0 #rules: 0 #arcs: 1/4