/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: a__f(0()) -> cons(0(),f(s(0()))) a__f(s(0())) -> a__f(a__p(s(0()))) a__p(s(0())) -> 0() mark(f(X)) -> a__f(mark(X)) mark(p(X)) -> a__p(mark(X)) mark(0()) -> 0() mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) a__f(X) -> f(X) a__p(X) -> p(X) Proof: Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [p](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1] [mark](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 1 0] [a__p](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [f](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [s](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [a__f](x0) = [0 0 1]x0 [0 1 1] , [0] [0] = [0] [0] orientation: [0] [0] a__f(0()) = [0] >= [0] = cons(0(),f(s(0()))) [0] [0] [0] [0] a__f(s(0())) = [0] >= [0] = a__f(a__p(s(0()))) [0] [0] [0] [0] a__p(s(0())) = [0] >= [0] = 0() [0] [0] [1 0 0] [1] [1 0 0] [1] mark(f(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = a__f(mark(X)) [0 0 0] [0] [0 0 0] [0] [1 1 0] [1] [1 0 0] [1] mark(p(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = a__p(mark(X)) [0 0 0] [0] [0 0 0] [0] [1] [0] mark(0()) = [0] >= [0] = 0() [0] [0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] mark(cons(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = cons(mark(X1),X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] mark(s(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = s(mark(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] a__f(X) = [0 0 1]X >= [0 0 0]X = f(X) [0 1 1] [0 0 0] [1 1 0] [1 1 0] a__p(X) = [0 0 0]X >= [0 0 0]X = p(X) [0 0 0] [0 0 0] problem: a__f(0()) -> cons(0(),f(s(0()))) a__f(s(0())) -> a__f(a__p(s(0()))) a__p(s(0())) -> 0() mark(f(X)) -> a__f(mark(X)) mark(p(X)) -> a__p(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) a__f(X) -> f(X) a__p(X) -> p(X) Matrix Interpretation Processor: dim=1 interpretation: [p](x0) = x0, [mark](x0) = 4x0, [a__p](x0) = x0, [cons](x0, x1) = x0 + 2x1, [f](x0) = 4x0 + 2, [s](x0) = 2x0, [a__f](x0) = 4x0 + 4, [0] = 0 orientation: a__f(0()) = 4 >= 4 = cons(0(),f(s(0()))) a__f(s(0())) = 4 >= 4 = a__f(a__p(s(0()))) a__p(s(0())) = 0 >= 0 = 0() mark(f(X)) = 16X + 8 >= 16X + 4 = a__f(mark(X)) mark(p(X)) = 4X >= 4X = a__p(mark(X)) mark(cons(X1,X2)) = 4X1 + 8X2 >= 4X1 + 2X2 = cons(mark(X1),X2) mark(s(X)) = 8X >= 8X = s(mark(X)) a__f(X) = 4X + 4 >= 4X + 2 = f(X) a__p(X) = X >= X = p(X) problem: a__f(0()) -> cons(0(),f(s(0()))) a__f(s(0())) -> a__f(a__p(s(0()))) a__p(s(0())) -> 0() mark(p(X)) -> a__p(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) a__p(X) -> p(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [p](x0) = [0 1 0]x0 [0 0 0] , [1 1 0] [1] [mark](x0) = [0 1 0]x0 + [0] [0 0 1] [0], [1 0 0] [a__p](x0) = [0 1 0]x0 [0 0 0] , [1 0 1] [cons](x0, x1) = x0 + [0 0 0]x1 [0 0 0] , [1 0 0] [f](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [s](x0) = [0 1 0]x0 [0 0 0] , [1 0 0] [1] [a__f](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [0] [0] = [0] [0] orientation: [1] [0] a__f(0()) = [0] >= [0] = cons(0(),f(s(0()))) [0] [0] [1] [1] a__f(s(0())) = [0] >= [0] = a__f(a__p(s(0()))) [0] [0] [0] [0] a__p(s(0())) = [0] >= [0] = 0() [0] [0] [1 1 0] [1] [1 1 0] [1] mark(p(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = a__p(mark(X)) [0 0 0] [0] [0 0 0] [0] [1 1 0] [1 0 1] [1] [1 1 0] [1 0 1] [1] mark(cons(X1,X2)) = [0 1 0]X1 + [0 0 0]X2 + [0] >= [0 1 0]X1 + [0 0 0]X2 + [0] = cons(mark(X1),X2) [0 0 1] [0 0 0] [0] [0 0 1] [0 0 0] [0] [1 1 0] [1] [1 1 0] [1] mark(s(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = s(mark(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] a__p(X) = [0 1 0]X >= [0 1 0]X = p(X) [0 0 0] [0 0 0] problem: a__f(s(0())) -> a__f(a__p(s(0()))) a__p(s(0())) -> 0() mark(p(X)) -> a__p(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) a__p(X) -> p(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [p](x0) = [0 0 0]x0 [0 0 1] , [1 0 1] [mark](x0) = [0 1 0]x0 [0 0 0] , [1 0 0] [a__p](x0) = [0 0 0]x0 [0 0 1] , [1 0 1] [1 0 0] [0] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 0 0] [0 0 0] [0], [1 1 0] [s](x0) = [0 0 1]x0 [0 0 1] , [1 1 0] [a__f](x0) = [0 0 0]x0 [0 0 0] , [0] [0] = [0] [1] orientation: [1] [0] a__f(s(0())) = [0] >= [0] = a__f(a__p(s(0()))) [0] [0] [0] [0] a__p(s(0())) = [0] >= [0] = 0() [1] [1] [1 0 1] [1 0 1] mark(p(X)) = [0 0 0]X >= [0 0 0]X = a__p(mark(X)) [0 0 0] [0 0 0] [1 0 1] [1 0 0] [0] [1 0 1] [1 0 0] [0] mark(cons(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = cons(mark(X1),X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 1] [1 1 1] mark(s(X)) = [0 0 1]X >= [0 0 0]X = s(mark(X)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] a__p(X) = [0 0 0]X >= [0 0 0]X = p(X) [0 0 1] [0 0 1] problem: a__p(s(0())) -> 0() mark(p(X)) -> a__p(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) a__p(X) -> p(X) Matrix Interpretation Processor: dim=1 interpretation: [p](x0) = 2x0 + 2, [mark](x0) = 4x0, [a__p](x0) = 2x0 + 2, [cons](x0, x1) = 4x0 + 2x1 + 4, [s](x0) = 2x0, [0] = 4 orientation: a__p(s(0())) = 18 >= 4 = 0() mark(p(X)) = 8X + 8 >= 8X + 2 = a__p(mark(X)) mark(cons(X1,X2)) = 16X1 + 8X2 + 16 >= 16X1 + 2X2 + 4 = cons(mark(X1),X2) mark(s(X)) = 8X >= 8X = s(mark(X)) a__p(X) = 2X + 2 >= 2X + 2 = p(X) problem: mark(s(X)) -> s(mark(X)) a__p(X) -> p(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [p](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [mark](x0) = [0 0 1]x0 [0 0 1] , [1 0 0] [1] [a__p](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [0] [s](x0) = [0 0 0]x0 + [0] [0 0 1] [1] orientation: [1 0 1] [1] [1 0 1] [0] mark(s(X)) = [0 0 1]X + [1] >= [0 0 0]X + [0] = s(mark(X)) [0 0 1] [1] [0 0 1] [1] [1 0 0] [1] [1 0 0] a__p(X) = [0 0 0]X + [0] >= [0 0 0]X = p(X) [0 0 0] [0] [0 0 0] problem: Qed