/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(take(0(),XS)) -> mark(nil()) active(take(s(N),cons(X,XS))) -> mark(cons(X,take(N,XS))) active(zip(nil(),XS)) -> mark(nil()) active(zip(X,nil())) -> mark(nil()) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(tail(cons(X,XS))) -> mark(XS) active(repItems(nil())) -> mark(nil()) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) mark(pairNs()) -> active(pairNs()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(oddNs()) -> active(oddNs()) mark(s(X)) -> active(s(mark(X))) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(zip(X1,X2)) -> active(zip(mark(X1),mark(X2))) mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2))) mark(tail(X)) -> active(tail(mark(X))) mark(repItems(X)) -> active(repItems(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) zip(mark(X1),X2) -> zip(X1,X2) zip(X1,mark(X2)) -> zip(X1,X2) zip(active(X1),X2) -> zip(X1,X2) zip(X1,active(X2)) -> zip(X1,X2) pair(mark(X1),X2) -> pair(X1,X2) pair(X1,mark(X2)) -> pair(X1,X2) pair(active(X1),X2) -> pair(X1,X2) pair(X1,active(X2)) -> pair(X1,X2) tail(mark(X)) -> tail(X) tail(active(X)) -> tail(X) repItems(mark(X)) -> repItems(X) repItems(active(X)) -> repItems(X) Proof: Matrix Interpretation Processor: dim=1 interpretation: [incr](x0) = x0, [take](x0, x1) = 4x0 + x1 + 4, [active](x0) = x0, [oddNs] = 0, [cons](x0, x1) = 4x0 + x1, [zip](x0, x1) = 4x0 + 4x1, [pairNs] = 0, [s](x0) = x0, [tail](x0) = x0 + 6, [pair](x0, x1) = x0 + 3x1, [nil] = 2, [repItems](x0) = 2x0, [mark](x0) = x0, [0] = 0 orientation: active(pairNs()) = 0 >= 0 = mark(cons(0(),incr(oddNs()))) active(oddNs()) = 0 >= 0 = mark(incr(pairNs())) active(incr(cons(X,XS))) = 4X + XS >= 4X + XS = mark(cons(s(X),incr(XS))) active(take(0(),XS)) = XS + 4 >= 2 = mark(nil()) active(take(s(N),cons(X,XS))) = 4N + 4X + XS + 4 >= 4N + 4X + XS + 4 = mark(cons(X,take(N,XS))) active(zip(nil(),XS)) = 4XS + 8 >= 2 = mark(nil()) active(zip(X,nil())) = 4X + 8 >= 2 = mark(nil()) active(zip(cons(X,XS),cons(Y,YS))) = 16X + 4XS + 16Y + 4YS >= 4X + 4XS + 12Y + 4YS = mark(cons(pair(X,Y),zip(XS,YS))) active(tail(cons(X,XS))) = 4X + XS + 6 >= XS = mark(XS) active(repItems(nil())) = 4 >= 2 = mark(nil()) active(repItems(cons(X,XS))) = 8X + 2XS >= 8X + 2XS = mark(cons(X,cons(X,repItems(XS)))) mark(pairNs()) = 0 >= 0 = active(pairNs()) mark(cons(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(incr(X)) = X >= X = active(incr(mark(X))) mark(oddNs()) = 0 >= 0 = active(oddNs()) mark(s(X)) = X >= X = active(s(mark(X))) mark(take(X1,X2)) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = active(take(mark(X1),mark(X2))) mark(nil()) = 2 >= 2 = active(nil()) mark(zip(X1,X2)) = 4X1 + 4X2 >= 4X1 + 4X2 = active(zip(mark(X1),mark(X2))) mark(pair(X1,X2)) = X1 + 3X2 >= X1 + 3X2 = active(pair(mark(X1),mark(X2))) mark(tail(X)) = X + 6 >= X + 6 = active(tail(mark(X))) mark(repItems(X)) = 2X >= 2X = active(repItems(mark(X))) cons(mark(X1),X2) = 4X1 + X2 >= 4X1 + X2 = cons(X1,X2) cons(X1,mark(X2)) = 4X1 + X2 >= 4X1 + X2 = cons(X1,X2) cons(active(X1),X2) = 4X1 + X2 >= 4X1 + X2 = cons(X1,X2) cons(X1,active(X2)) = 4X1 + X2 >= 4X1 + X2 = cons(X1,X2) incr(mark(X)) = X >= X = incr(X) incr(active(X)) = X >= X = incr(X) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) take(mark(X1),X2) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = take(X1,X2) take(X1,mark(X2)) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = take(X1,X2) take(active(X1),X2) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = take(X1,X2) take(X1,active(X2)) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = take(X1,X2) zip(mark(X1),X2) = 4X1 + 4X2 >= 4X1 + 4X2 = zip(X1,X2) zip(X1,mark(X2)) = 4X1 + 4X2 >= 4X1 + 4X2 = zip(X1,X2) zip(active(X1),X2) = 4X1 + 4X2 >= 4X1 + 4X2 = zip(X1,X2) zip(X1,active(X2)) = 4X1 + 4X2 >= 4X1 + 4X2 = zip(X1,X2) pair(mark(X1),X2) = X1 + 3X2 >= X1 + 3X2 = pair(X1,X2) pair(X1,mark(X2)) = X1 + 3X2 >= X1 + 3X2 = pair(X1,X2) pair(active(X1),X2) = X1 + 3X2 >= X1 + 3X2 = pair(X1,X2) pair(X1,active(X2)) = X1 + 3X2 >= X1 + 3X2 = pair(X1,X2) tail(mark(X)) = X + 6 >= X + 6 = tail(X) tail(active(X)) = X + 6 >= X + 6 = tail(X) repItems(mark(X)) = 2X >= 2X = repItems(X) repItems(active(X)) = 2X >= 2X = repItems(X) problem: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(take(s(N),cons(X,XS))) -> mark(cons(X,take(N,XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) mark(pairNs()) -> active(pairNs()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(oddNs()) -> active(oddNs()) mark(s(X)) -> active(s(mark(X))) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(zip(X1,X2)) -> active(zip(mark(X1),mark(X2))) mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2))) mark(tail(X)) -> active(tail(mark(X))) mark(repItems(X)) -> active(repItems(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) zip(mark(X1),X2) -> zip(X1,X2) zip(X1,mark(X2)) -> zip(X1,X2) zip(active(X1),X2) -> zip(X1,X2) zip(X1,active(X2)) -> zip(X1,X2) pair(mark(X1),X2) -> pair(X1,X2) pair(X1,mark(X2)) -> pair(X1,X2) pair(active(X1),X2) -> pair(X1,X2) pair(X1,active(X2)) -> pair(X1,X2) tail(mark(X)) -> tail(X) tail(active(X)) -> tail(X) repItems(mark(X)) -> repItems(X) repItems(active(X)) -> repItems(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [incr](x0) = [1 0 0]x0 [1 0 0] , [1 1 0] [1 0 0] [1] [take](x0, x1) = [1 1 0]x0 + [1 1 0]x1 + [1] [0 1 0] [1 1 0] [1], [active](x0) = x0 , [0] [oddNs] = [0] [0], [1 0 0] [1 0 0] [cons](x0, x1) = [1 0 0]x0 + [0 1 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [zip](x0, x1) = [0 1 0]x0 + [1 0 0]x1 [0 1 0] [1 0 0] , [0] [pairNs] = [0] [0], [1 0 0] [0] [s](x0) = [1 1 0]x0 + [1] [0 0 0] [0], [1 1 0] [0] [tail](x0) = [0 1 0]x0 + [1] [0 0 0] [1], [1 0 0] [1 0 0] [pair](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [0] [nil] = [0] [0], [1 1 0] [repItems](x0) = [1 1 0]x0 [1 1 0] , [1 0 0] [mark](x0) = [0 1 0]x0 [0 1 0] , [0] [0] = [1] [1] orientation: [0] [0] active(pairNs()) = [0] >= [0] = mark(cons(0(),incr(oddNs()))) [0] [0] [0] [0] active(oddNs()) = [0] >= [0] = mark(incr(pairNs())) [0] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(incr(cons(X,XS))) = [1 0 0]X + [1 0 0]XS >= [1 0 0]X + [1 0 0]XS = mark(cons(s(X),incr(XS))) [1 0 0] [1 0 0] [1 0 0] [1 0 0] [2 1 0] [1 0 0] [1 0 0] [2] [1 1 0] [1 0 0] [1 0 0] [1] active(take(s(N),cons(X,XS))) = [2 1 0]N + [2 0 0]X + [1 1 0]XS + [2] >= [1 1 0]N + [1 0 0]X + [1 1 0]XS + [1] = mark(cons(X,take(N,XS))) [1 1 0] [2 0 0] [1 1 0] [2] [1 1 0] [1 0 0] [1 1 0] [1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] active(zip(cons(X,XS),cons(Y,YS))) = [1 0 0]X + [0 1 0]XS + [1 0 0]Y + [1 0 0]YS >= [1 0 0]X + [0 1 0]XS + [1 0 0]Y + [1 0 0]YS = mark(cons(pair(X,Y),zip(XS,YS))) [1 0 0] [0 1 0] [1 0 0] [1 0 0] [1 0 0] [0 1 0] [1 0 0] [1 0 0] [2 0 0] [1 1 0] [2 0 0] [1 1 0] active(repItems(cons(X,XS))) = [2 0 0]X + [1 1 0]XS >= [2 0 0]X + [1 1 0]XS = mark(cons(X,cons(X,repItems(XS)))) [2 0 0] [1 1 0] [2 0 0] [1 1 0] [0] [0] mark(pairNs()) = [0] >= [0] = active(pairNs()) [0] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] mark(cons(X1,X2)) = [1 0 0]X1 + [0 1 0]X2 >= [1 0 0]X1 + [0 1 0]X2 = active(cons(mark(X1),X2)) [1 0 0] [0 1 0] [0 0 0] [0 0 0] [0] [0] mark(0()) = [1] >= [1] = active(0()) [1] [1] [1 0 0] [1 0 0] mark(incr(X)) = [1 0 0]X >= [1 0 0]X = active(incr(mark(X))) [1 0 0] [1 0 0] [0] [0] mark(oddNs()) = [0] >= [0] = active(oddNs()) [0] [0] [1 0 0] [0] [1 0 0] [0] mark(s(X)) = [1 1 0]X + [1] >= [1 1 0]X + [1] = active(s(mark(X))) [1 1 0] [1] [0 0 0] [0] [1 1 0] [1 0 0] [1] [1 1 0] [1 0 0] [1] mark(take(X1,X2)) = [1 1 0]X1 + [1 1 0]X2 + [1] >= [1 1 0]X1 + [1 1 0]X2 + [1] = active(take(mark(X1),mark(X2))) [1 1 0] [1 1 0] [1] [0 1 0] [1 1 0] [1] [0] [0] mark(nil()) = [0] >= [0] = active(nil()) [0] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] mark(zip(X1,X2)) = [0 1 0]X1 + [1 0 0]X2 >= [0 1 0]X1 + [1 0 0]X2 = active(zip(mark(X1),mark(X2))) [0 1 0] [1 0 0] [0 1 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] mark(pair(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = active(pair(mark(X1),mark(X2))) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [0] [1 1 0] [0] mark(tail(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = active(tail(mark(X))) [0 1 0] [1] [0 0 0] [1] [1 1 0] [1 1 0] mark(repItems(X)) = [1 1 0]X >= [1 1 0]X = active(repItems(mark(X))) [1 1 0] [1 1 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] cons(mark(X1),X2) = [1 0 0]X1 + [0 1 0]X2 >= [1 0 0]X1 + [0 1 0]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] cons(X1,mark(X2)) = [1 0 0]X1 + [0 1 0]X2 >= [1 0 0]X1 + [0 1 0]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] cons(active(X1),X2) = [1 0 0]X1 + [0 1 0]X2 >= [1 0 0]X1 + [0 1 0]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] cons(X1,active(X2)) = [1 0 0]X1 + [0 1 0]X2 >= [1 0 0]X1 + [0 1 0]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] incr(mark(X)) = [1 0 0]X >= [1 0 0]X = incr(X) [1 0 0] [1 0 0] [1 0 0] [1 0 0] incr(active(X)) = [1 0 0]X >= [1 0 0]X = incr(X) [1 0 0] [1 0 0] [1 0 0] [0] [1 0 0] [0] s(mark(X)) = [1 1 0]X + [1] >= [1 1 0]X + [1] = s(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [0] [1 0 0] [0] s(active(X)) = [1 1 0]X + [1] >= [1 1 0]X + [1] = s(X) [0 0 0] [0] [0 0 0] [0] [1 1 0] [1 0 0] [1] [1 1 0] [1 0 0] [1] take(mark(X1),X2) = [1 1 0]X1 + [1 1 0]X2 + [1] >= [1 1 0]X1 + [1 1 0]X2 + [1] = take(X1,X2) [0 1 0] [1 1 0] [1] [0 1 0] [1 1 0] [1] [1 1 0] [1 0 0] [1] [1 1 0] [1 0 0] [1] take(X1,mark(X2)) = [1 1 0]X1 + [1 1 0]X2 + [1] >= [1 1 0]X1 + [1 1 0]X2 + [1] = take(X1,X2) [0 1 0] [1 1 0] [1] [0 1 0] [1 1 0] [1] [1 1 0] [1 0 0] [1] [1 1 0] [1 0 0] [1] take(active(X1),X2) = [1 1 0]X1 + [1 1 0]X2 + [1] >= [1 1 0]X1 + [1 1 0]X2 + [1] = take(X1,X2) [0 1 0] [1 1 0] [1] [0 1 0] [1 1 0] [1] [1 1 0] [1 0 0] [1] [1 1 0] [1 0 0] [1] take(X1,active(X2)) = [1 1 0]X1 + [1 1 0]X2 + [1] >= [1 1 0]X1 + [1 1 0]X2 + [1] = take(X1,X2) [0 1 0] [1 1 0] [1] [0 1 0] [1 1 0] [1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] zip(mark(X1),X2) = [0 1 0]X1 + [1 0 0]X2 >= [0 1 0]X1 + [1 0 0]X2 = zip(X1,X2) [0 1 0] [1 0 0] [0 1 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] zip(X1,mark(X2)) = [0 1 0]X1 + [1 0 0]X2 >= [0 1 0]X1 + [1 0 0]X2 = zip(X1,X2) [0 1 0] [1 0 0] [0 1 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] zip(active(X1),X2) = [0 1 0]X1 + [1 0 0]X2 >= [0 1 0]X1 + [1 0 0]X2 = zip(X1,X2) [0 1 0] [1 0 0] [0 1 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] zip(X1,active(X2)) = [0 1 0]X1 + [1 0 0]X2 >= [0 1 0]X1 + [1 0 0]X2 = zip(X1,X2) [0 1 0] [1 0 0] [0 1 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] pair(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = pair(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] pair(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = pair(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] pair(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = pair(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] pair(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = pair(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [0] [1 1 0] [0] tail(mark(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = tail(X) [0 0 0] [1] [0 0 0] [1] [1 1 0] [0] [1 1 0] [0] tail(active(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = tail(X) [0 0 0] [1] [0 0 0] [1] [1 1 0] [1 1 0] repItems(mark(X)) = [1 1 0]X >= [1 1 0]X = repItems(X) [1 1 0] [1 1 0] [1 1 0] [1 1 0] repItems(active(X)) = [1 1 0]X >= [1 1 0]X = repItems(X) [1 1 0] [1 1 0] problem: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) mark(pairNs()) -> active(pairNs()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(oddNs()) -> active(oddNs()) mark(s(X)) -> active(s(mark(X))) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(zip(X1,X2)) -> active(zip(mark(X1),mark(X2))) mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2))) mark(tail(X)) -> active(tail(mark(X))) mark(repItems(X)) -> active(repItems(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) zip(mark(X1),X2) -> zip(X1,X2) zip(X1,mark(X2)) -> zip(X1,X2) zip(active(X1),X2) -> zip(X1,X2) zip(X1,active(X2)) -> zip(X1,X2) pair(mark(X1),X2) -> pair(X1,X2) pair(X1,mark(X2)) -> pair(X1,X2) pair(active(X1),X2) -> pair(X1,X2) pair(X1,active(X2)) -> pair(X1,X2) tail(mark(X)) -> tail(X) tail(active(X)) -> tail(X) repItems(mark(X)) -> repItems(X) repItems(active(X)) -> repItems(X) Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [incr](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [1 1 0] [1] [take](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 0 0] [0 0 0] [0], [1 1 0] [0] [active](x0) = [0 0 0]x0 + [0] [0 0 1] [1], [0] [oddNs] = [0] [0], [1 1 0] [1 1 1] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 1 0] [1 1 0] [zip](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [0] [pairNs] = [0] [0], [1 1 0] [s](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [0] [tail](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 1 0] [1 1 0] [pair](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [0] [nil] = [0] [0], [1 1 0] [repItems](x0) = [1 1 0]x0 [0 0 0] , [1 1 0] [0] [mark](x0) = [0 0 0]x0 + [0] [0 0 1] [1], [0] [0] = [0] [0] orientation: [0] [0] active(pairNs()) = [0] >= [0] = mark(cons(0(),incr(oddNs()))) [1] [1] [0] [0] active(oddNs()) = [0] >= [0] = mark(incr(pairNs())) [1] [1] [1 1 0] [1 1 1] [0] [1 1 0] [1 1 0] [0] active(incr(cons(X,XS))) = [0 0 0]X + [0 0 0]XS + [0] >= [0 0 0]X + [0 0 0]XS + [0] = mark(cons(s(X),incr(XS))) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 1 0] [1 1 1] [1 1 0] [1 1 1] [0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] [0] active(zip(cons(X,XS),cons(Y,YS))) = [0 0 0]X + [0 0 0]XS + [0 0 0]Y + [0 0 0]YS + [0] >= [0 0 0]X + [0 0 0]XS + [0 0 0]Y + [0 0 0]YS + [0] = mark(cons(pair(X,Y),zip(XS,YS))) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1] [2 2 0] [2 2 2] [0] [2 2 0] [2 2 0] [0] active(repItems(cons(X,XS))) = [0 0 0]X + [0 0 0]XS + [0] >= [0 0 0]X + [0 0 0]XS + [0] = mark(cons(X,cons(X,repItems(XS)))) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [0] [0] mark(pairNs()) = [0] >= [0] = active(pairNs()) [1] [1] [1 1 0] [1 1 1] [0] [1 1 0] [1 1 1] [0] mark(cons(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(cons(mark(X1),X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [0] [0] mark(0()) = [0] >= [0] = active(0()) [1] [1] [1 1 0] [0] [1 1 0] [0] mark(incr(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(incr(mark(X))) [0 0 0] [1] [0 0 0] [1] [0] [0] mark(oddNs()) = [0] >= [0] = active(oddNs()) [1] [1] [1 1 0] [0] [1 1 0] [0] mark(s(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(s(mark(X))) [0 0 0] [1] [0 0 0] [1] [1 1 0] [1 1 0] [2] [1 1 0] [1 1 0] [2] mark(take(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(take(mark(X1),mark(X2))) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [0] [0] mark(nil()) = [0] >= [0] = active(nil()) [1] [1] [1 1 0] [1 1 0] [0] [1 1 0] [1 1 0] [0] mark(zip(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(zip(mark(X1),mark(X2))) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 1 0] [1 1 0] [0] [1 1 0] [1 1 0] [0] mark(pair(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(pair(mark(X1),mark(X2))) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 1 0] [0] [1 1 0] [0] mark(tail(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(tail(mark(X))) [0 0 0] [2] [0 0 0] [2] [2 2 0] [0] [2 2 0] [0] mark(repItems(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(repItems(mark(X))) [0 0 0] [1] [0 0 0] [1] [1 1 0] [1 1 1] [1 1 0] [1 1 1] cons(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 1] [1] [1 1 0] [1 1 1] cons(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 1 0] [1 1 1] [1 1 0] [1 1 1] cons(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 1] [1] [1 1 0] [1 1 1] cons(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] incr(mark(X)) = [0 0 0]X >= [0 0 0]X = incr(X) [0 0 0] [0 0 0] [1 1 0] [1 1 0] incr(active(X)) = [0 0 0]X >= [0 0 0]X = incr(X) [0 0 0] [0 0 0] [1 1 0] [1 1 0] s(mark(X)) = [0 0 0]X >= [0 0 0]X = s(X) [0 0 0] [0 0 0] [1 1 0] [1 1 0] s(active(X)) = [0 0 0]X >= [0 0 0]X = s(X) [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1] [1 1 0] [1 1 0] [1] take(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = take(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [1 1 0] [1] [1 1 0] [1 1 0] [1] take(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = take(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [1 1 0] [1] [1 1 0] [1 1 0] [1] take(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = take(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [1 1 0] [1] [1 1 0] [1 1 0] [1] take(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = take(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] zip(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = zip(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] zip(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = zip(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] zip(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = zip(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] zip(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = zip(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] pair(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = pair(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] pair(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = pair(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] pair(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = pair(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] pair(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = pair(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [0] [1 1 0] [0] tail(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = tail(X) [0 0 0] [1] [0 0 0] [1] [1 1 0] [0] [1 1 0] [0] tail(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = tail(X) [0 0 0] [1] [0 0 0] [1] [1 1 0] [1 1 0] repItems(mark(X)) = [1 1 0]X >= [1 1 0]X = repItems(X) [0 0 0] [0 0 0] [1 1 0] [1 1 0] repItems(active(X)) = [1 1 0]X >= [1 1 0]X = repItems(X) [0 0 0] [0 0 0] problem: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) mark(pairNs()) -> active(pairNs()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(oddNs()) -> active(oddNs()) mark(s(X)) -> active(s(mark(X))) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(zip(X1,X2)) -> active(zip(mark(X1),mark(X2))) mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2))) mark(tail(X)) -> active(tail(mark(X))) mark(repItems(X)) -> active(repItems(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) zip(mark(X1),X2) -> zip(X1,X2) zip(X1,mark(X2)) -> zip(X1,X2) zip(active(X1),X2) -> zip(X1,X2) zip(X1,active(X2)) -> zip(X1,X2) pair(mark(X1),X2) -> pair(X1,X2) pair(X1,mark(X2)) -> pair(X1,X2) pair(active(X1),X2) -> pair(X1,X2) pair(X1,active(X2)) -> pair(X1,X2) tail(mark(X)) -> tail(X) tail(active(X)) -> tail(X) repItems(mark(X)) -> repItems(X) repItems(active(X)) -> repItems(X) Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [incr](x0) = [0 1 1]x0 [0 0 0] , [1 1 0] [1 1 0] [take](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 1 0] [active](x0) = [0 0 0]x0 [0 1 1] , [0] [oddNs] = [0] [0], [1 1 0] [1 0 0] [cons](x0, x1) = [1 1 0]x0 + [0 0 0]x1 [0 0 0] [0 1 1] , [1 1 0] [1 1 0] [zip](x0, x1) = [0 1 1]x0 + [0 1 1]x1 [0 0 0] [0 0 0] , [0] [pairNs] = [0] [0], [1 1 0] [s](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [tail](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [1 1 0] [pair](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1] [nil] = [0] [0], [1 1 0] [0] [repItems](x0) = [0 1 1]x0 + [1] [0 1 1] [0], [1 1 0] [mark](x0) = [0 0 0]x0 [0 1 1] , [0] [0] = [0] [0] orientation: [0] [0] active(pairNs()) = [0] >= [0] = mark(cons(0(),incr(oddNs()))) [0] [0] [0] [0] active(oddNs()) = [0] >= [0] = mark(incr(pairNs())) [0] [0] [3 3 0] [1 1 1] [2 2 0] [1 1 0] active(incr(cons(X,XS))) = [0 0 0]X + [0 0 0]XS >= [0 0 0]X + [0 0 0]XS = mark(cons(s(X),incr(XS))) [1 1 0] [0 1 1] [1 1 0] [0 1 1] [3 3 0] [1 1 1] [3 3 0] [1 1 1] [2 2 0] [1 1 0] [2 2 0] [1 1 0] active(zip(cons(X,XS),cons(Y,YS))) = [0 0 0]X + [0 0 0]XS + [0 0 0]Y + [0 0 0]YS >= [0 0 0]X + [0 0 0]XS + [0 0 0]Y + [0 0 0]YS = mark(cons(pair(X,Y),zip(XS,YS))) [1 1 0] [0 1 1] [1 1 0] [0 1 1] [1 1 0] [0 1 1] [1 1 0] [0 1 1] [3 3 0] [1 1 1] [1] [3 3 0] [1 1 0] [0] active(repItems(cons(X,XS))) = [0 0 0]X + [0 0 0]XS + [0] >= [0 0 0]X + [0 0 0]XS + [0] = mark(cons(X,cons(X,repItems(XS)))) [2 2 0] [0 2 2] [1] [2 2 0] [0 2 2] [1] [0] [0] mark(pairNs()) = [0] >= [0] = active(pairNs()) [0] [0] [2 2 0] [1 0 0] [2 2 0] [1 0 0] mark(cons(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = active(cons(mark(X1),X2)) [1 1 0] [0 1 1] [1 1 0] [0 1 1] [0] [0] mark(0()) = [0] >= [0] = active(0()) [0] [0] [1 2 1] [1 2 1] mark(incr(X)) = [0 0 0]X >= [0 0 0]X = active(incr(mark(X))) [0 1 1] [0 1 1] [0] [0] mark(oddNs()) = [0] >= [0] = active(oddNs()) [0] [0] [1 1 0] [1 1 0] mark(s(X)) = [0 0 0]X >= [0 0 0]X = active(s(mark(X))) [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] mark(take(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = active(take(mark(X1),mark(X2))) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1] [1] mark(nil()) = [0] >= [0] = active(nil()) [0] [0] [1 2 1] [1 2 1] [1 2 1] [1 2 1] mark(zip(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = active(zip(mark(X1),mark(X2))) [0 1 1] [0 1 1] [0 1 1] [0 1 1] [1 1 0] [1 1 0] [1 1 0] [1 1 0] mark(pair(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = active(pair(mark(X1),mark(X2))) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] mark(tail(X)) = [0 0 0]X >= [0 0 0]X = active(tail(mark(X))) [0 0 0] [0 0 0] [1 2 1] [1] [1 2 1] [1] mark(repItems(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(repItems(mark(X))) [0 2 2] [1] [0 2 2] [1] [1 1 0] [1 0 0] [1 1 0] [1 0 0] cons(mark(X1),X2) = [1 1 0]X1 + [0 0 0]X2 >= [1 1 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1 1 0] [1 0 0] [1 1 0] [1 0 0] cons(active(X1),X2) = [1 1 0]X1 + [0 0 0]X2 >= [1 1 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1 1 0] [1 1 0] incr(mark(X)) = [0 1 1]X >= [0 1 1]X = incr(X) [0 0 0] [0 0 0] [1 1 0] [1 1 0] incr(active(X)) = [0 1 1]X >= [0 1 1]X = incr(X) [0 0 0] [0 0 0] [1 1 0] [1 1 0] s(mark(X)) = [0 0 0]X >= [0 0 0]X = s(X) [0 0 0] [0 0 0] [1 1 0] [1 1 0] s(active(X)) = [0 0 0]X >= [0 0 0]X = s(X) [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] take(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = take(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] take(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = take(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] take(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = take(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] take(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = take(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] zip(mark(X1),X2) = [0 1 1]X1 + [0 1 1]X2 >= [0 1 1]X1 + [0 1 1]X2 = zip(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] zip(X1,mark(X2)) = [0 1 1]X1 + [0 1 1]X2 >= [0 1 1]X1 + [0 1 1]X2 = zip(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] zip(active(X1),X2) = [0 1 1]X1 + [0 1 1]X2 >= [0 1 1]X1 + [0 1 1]X2 = zip(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] zip(X1,active(X2)) = [0 1 1]X1 + [0 1 1]X2 >= [0 1 1]X1 + [0 1 1]X2 = zip(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] pair(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = pair(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] pair(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = pair(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] pair(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = pair(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] pair(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = pair(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] tail(mark(X)) = [0 0 0]X >= [0 0 0]X = tail(X) [0 0 0] [0 0 0] [1 1 0] [1 1 0] tail(active(X)) = [0 0 0]X >= [0 0 0]X = tail(X) [0 0 0] [0 0 0] [1 1 0] [0] [1 1 0] [0] repItems(mark(X)) = [0 1 1]X + [1] >= [0 1 1]X + [1] = repItems(X) [0 1 1] [0] [0 1 1] [0] [1 1 0] [0] [1 1 0] [0] repItems(active(X)) = [0 1 1]X + [1] >= [0 1 1]X + [1] = repItems(X) [0 1 1] [0] [0 1 1] [0] problem: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) mark(pairNs()) -> active(pairNs()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(oddNs()) -> active(oddNs()) mark(s(X)) -> active(s(mark(X))) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(zip(X1,X2)) -> active(zip(mark(X1),mark(X2))) mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2))) mark(tail(X)) -> active(tail(mark(X))) mark(repItems(X)) -> active(repItems(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) zip(mark(X1),X2) -> zip(X1,X2) zip(X1,mark(X2)) -> zip(X1,X2) zip(active(X1),X2) -> zip(X1,X2) zip(X1,active(X2)) -> zip(X1,X2) pair(mark(X1),X2) -> pair(X1,X2) pair(X1,mark(X2)) -> pair(X1,X2) pair(active(X1),X2) -> pair(X1,X2) pair(X1,active(X2)) -> pair(X1,X2) tail(mark(X)) -> tail(X) tail(active(X)) -> tail(X) repItems(mark(X)) -> repItems(X) repItems(active(X)) -> repItems(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [incr](x0) = [0 1 0]x0 [0 0 1] , [1 0 0] [1 0 0] [take](x0, x1) = [0 1 0]x0 + [0 1 0]x1 [0 0 0] [0 0 0] , [active](x0) = x0 , [0] [oddNs] = [1] [0], [1 0 0] [1 0 0] [cons](x0, x1) = [0 1 0]x0 + [0 0 0]x1 [0 1 0] [0 0 1] , [1 0 1] [1 0 1] [zip](x0, x1) = [0 1 0]x0 + [0 1 0]x1 [0 0 1] [0 0 1] , [0] [pairNs] = [0] [0], [1 0 0] [s](x0) = [0 1 0]x0 [0 0 0] , [1 0 0] [tail](x0) = [0 1 0]x0 [0 1 0] , [1 0 0] [1 0 0] [pair](x0, x1) = [0 1 0]x0 + [0 1 0]x1 [0 0 0] [0 0 0] , [0] [nil] = [0] [0], [1 0 0] [1] [repItems](x0) = [0 1 0]x0 + [0] [0 0 0] [0], [1 1 0] [mark](x0) = [0 1 0]x0 [0 0 1] , [0] [0] = [0] [0] orientation: [0] [0] active(pairNs()) = [0] >= [0] = mark(cons(0(),incr(oddNs()))) [0] [0] [0] [0] active(oddNs()) = [1] >= [0] = mark(incr(pairNs())) [0] [0] [1 1 0] [1 0 1] [1 1 0] [1 0 1] active(incr(cons(X,XS))) = [0 1 0]X + [0 0 0]XS >= [0 1 0]X + [0 0 0]XS = mark(cons(s(X),incr(XS))) [0 1 0] [0 0 1] [0 1 0] [0 0 1] [1 1 0] [1 0 1] [1 1 0] [1 0 1] [1 1 0] [1 0 1] [1 1 0] [1 0 1] active(zip(cons(X,XS),cons(Y,YS))) = [0 1 0]X + [0 0 0]XS + [0 1 0]Y + [0 0 0]YS >= [0 1 0]X + [0 0 0]XS + [0 1 0]Y + [0 0 0]YS = mark(cons(pair(X,Y),zip(XS,YS))) [0 1 0] [0 0 1] [0 1 0] [0 0 1] [0 1 0] [0 0 1] [0 1 0] [0 0 1] [0] [0] mark(pairNs()) = [0] >= [0] = active(pairNs()) [0] [0] [1 1 0] [1 0 0] [1 1 0] [1 0 0] mark(cons(X1,X2)) = [0 1 0]X1 + [0 0 0]X2 >= [0 1 0]X1 + [0 0 0]X2 = active(cons(mark(X1),X2)) [0 1 0] [0 0 1] [0 1 0] [0 0 1] [0] [0] mark(0()) = [0] >= [0] = active(0()) [0] [0] [1 1 1] [1 1 1] mark(incr(X)) = [0 1 0]X >= [0 1 0]X = active(incr(mark(X))) [0 0 1] [0 0 1] [1] [0] mark(oddNs()) = [1] >= [1] = active(oddNs()) [0] [0] [1 1 0] [1 1 0] mark(s(X)) = [0 1 0]X >= [0 1 0]X = active(s(mark(X))) [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] mark(take(X1,X2)) = [0 1 0]X1 + [0 1 0]X2 >= [0 1 0]X1 + [0 1 0]X2 = active(take(mark(X1),mark(X2))) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0] [0] mark(nil()) = [0] >= [0] = active(nil()) [0] [0] [1 1 1] [1 1 1] [1 1 1] [1 1 1] mark(zip(X1,X2)) = [0 1 0]X1 + [0 1 0]X2 >= [0 1 0]X1 + [0 1 0]X2 = active(zip(mark(X1),mark(X2))) [0 0 1] [0 0 1] [0 0 1] [0 0 1] [1 1 0] [1 1 0] [1 1 0] [1 1 0] mark(pair(X1,X2)) = [0 1 0]X1 + [0 1 0]X2 >= [0 1 0]X1 + [0 1 0]X2 = active(pair(mark(X1),mark(X2))) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] mark(tail(X)) = [0 1 0]X >= [0 1 0]X = active(tail(mark(X))) [0 1 0] [0 1 0] [1 1 0] [1] [1 1 0] [1] mark(repItems(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = active(repItems(mark(X))) [0 0 0] [0] [0 0 0] [0] [1 1 0] [1 0 0] [1 0 0] [1 0 0] cons(mark(X1),X2) = [0 1 0]X1 + [0 0 0]X2 >= [0 1 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 1 0] [0 0 1] [0 1 0] [0 0 1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] cons(active(X1),X2) = [0 1 0]X1 + [0 0 0]X2 >= [0 1 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 1 0] [0 0 1] [0 1 0] [0 0 1] [1 1 1] [1 0 1] incr(mark(X)) = [0 1 0]X >= [0 1 0]X = incr(X) [0 0 1] [0 0 1] [1 0 1] [1 0 1] incr(active(X)) = [0 1 0]X >= [0 1 0]X = incr(X) [0 0 1] [0 0 1] [1 1 0] [1 0 0] s(mark(X)) = [0 1 0]X >= [0 1 0]X = s(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] s(active(X)) = [0 1 0]X >= [0 1 0]X = s(X) [0 0 0] [0 0 0] [1 1 0] [1 0 0] [1 0 0] [1 0 0] take(mark(X1),X2) = [0 1 0]X1 + [0 1 0]X2 >= [0 1 0]X1 + [0 1 0]X2 = take(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 1 0] [1 0 0] [1 0 0] take(X1,mark(X2)) = [0 1 0]X1 + [0 1 0]X2 >= [0 1 0]X1 + [0 1 0]X2 = take(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] take(active(X1),X2) = [0 1 0]X1 + [0 1 0]X2 >= [0 1 0]X1 + [0 1 0]X2 = take(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] take(X1,active(X2)) = [0 1 0]X1 + [0 1 0]X2 >= [0 1 0]X1 + [0 1 0]X2 = take(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 1] [1 0 1] [1 0 1] [1 0 1] zip(mark(X1),X2) = [0 1 0]X1 + [0 1 0]X2 >= [0 1 0]X1 + [0 1 0]X2 = zip(X1,X2) [0 0 1] [0 0 1] [0 0 1] [0 0 1] [1 0 1] [1 1 1] [1 0 1] [1 0 1] zip(X1,mark(X2)) = [0 1 0]X1 + [0 1 0]X2 >= [0 1 0]X1 + [0 1 0]X2 = zip(X1,X2) [0 0 1] [0 0 1] [0 0 1] [0 0 1] [1 0 1] [1 0 1] [1 0 1] [1 0 1] zip(active(X1),X2) = [0 1 0]X1 + [0 1 0]X2 >= [0 1 0]X1 + [0 1 0]X2 = zip(X1,X2) [0 0 1] [0 0 1] [0 0 1] [0 0 1] [1 0 1] [1 0 1] [1 0 1] [1 0 1] zip(X1,active(X2)) = [0 1 0]X1 + [0 1 0]X2 >= [0 1 0]X1 + [0 1 0]X2 = zip(X1,X2) [0 0 1] [0 0 1] [0 0 1] [0 0 1] [1 1 0] [1 0 0] [1 0 0] [1 0 0] pair(mark(X1),X2) = [0 1 0]X1 + [0 1 0]X2 >= [0 1 0]X1 + [0 1 0]X2 = pair(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 1 0] [1 0 0] [1 0 0] pair(X1,mark(X2)) = [0 1 0]X1 + [0 1 0]X2 >= [0 1 0]X1 + [0 1 0]X2 = pair(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] pair(active(X1),X2) = [0 1 0]X1 + [0 1 0]X2 >= [0 1 0]X1 + [0 1 0]X2 = pair(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] pair(X1,active(X2)) = [0 1 0]X1 + [0 1 0]X2 >= [0 1 0]X1 + [0 1 0]X2 = pair(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 0 0] tail(mark(X)) = [0 1 0]X >= [0 1 0]X = tail(X) [0 1 0] [0 1 0] [1 0 0] [1 0 0] tail(active(X)) = [0 1 0]X >= [0 1 0]X = tail(X) [0 1 0] [0 1 0] [1 1 0] [1] [1 0 0] [1] repItems(mark(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = repItems(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] repItems(active(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = repItems(X) [0 0 0] [0] [0 0 0] [0] problem: active(pairNs()) -> mark(cons(0(),incr(oddNs()))) active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) mark(pairNs()) -> active(pairNs()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(s(X)) -> active(s(mark(X))) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(zip(X1,X2)) -> active(zip(mark(X1),mark(X2))) mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2))) mark(tail(X)) -> active(tail(mark(X))) mark(repItems(X)) -> active(repItems(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) zip(mark(X1),X2) -> zip(X1,X2) zip(X1,mark(X2)) -> zip(X1,X2) zip(active(X1),X2) -> zip(X1,X2) zip(X1,active(X2)) -> zip(X1,X2) pair(mark(X1),X2) -> pair(X1,X2) pair(X1,mark(X2)) -> pair(X1,X2) pair(active(X1),X2) -> pair(X1,X2) pair(X1,active(X2)) -> pair(X1,X2) tail(mark(X)) -> tail(X) tail(active(X)) -> tail(X) repItems(mark(X)) -> repItems(X) repItems(active(X)) -> repItems(X) Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [incr](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [take](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 1] [0] [active](x0) = [0 1 0]x0 + [0] [0 0 0] [1], [0] [oddNs] = [0] [1], [1 0 0] [1 1 0] [cons](x0, x1) = [0 1 0]x0 + [0 0 1]x1 [0 0 0] [0 0 0] , [1 1 0] [1 0 0] [1] [zip](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [0], [1] [pairNs] = [0] [0], [1 0 0] [s](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [tail](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [pair](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1] [nil] = [0] [0], [1 0 0] [0] [repItems](x0) = [0 1 0]x0 + [1] [0 0 0] [0], [1 0 0] [0] [mark](x0) = [0 1 0]x0 + [0] [0 0 0] [1], [0] [0] = [0] [0] orientation: [1] [0] active(pairNs()) = [0] >= [0] = mark(cons(0(),incr(oddNs()))) [1] [1] [1] [1] active(oddNs()) = [0] >= [0] = mark(incr(pairNs())) [1] [1] [1 1 0] [1 1 1] [0] [1 0 0] [1 1 0] [0] active(incr(cons(X,XS))) = [0 0 0]X + [0 0 0]XS + [0] >= [0 0 0]X + [0 0 0]XS + [0] = mark(cons(s(X),incr(XS))) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 1 0] [1 1 1] [1 0 0] [1 1 0] [1] [1 0 0] [1 1 0] [1 0 0] [1 0 0] [1] active(zip(cons(X,XS),cons(Y,YS))) = [0 0 0]X + [0 0 0]XS + [0 0 0]Y + [0 0 0]YS + [0] >= [0 0 0]X + [0 0 0]XS + [0 0 0]Y + [0 0 0]YS + [0] = mark(cons(pair(X,Y),zip(XS,YS))) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1] [1] [1] mark(pairNs()) = [0] >= [0] = active(pairNs()) [1] [1] [1 0 0] [1 1 0] [0] [1 0 0] [1 1 0] [0] mark(cons(X1,X2)) = [0 1 0]X1 + [0 0 1]X2 + [0] >= [0 1 0]X1 + [0 0 1]X2 + [0] = active(cons(mark(X1),X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [0] [0] mark(0()) = [0] >= [0] = active(0()) [1] [1] [1 1 0] [0] [1 1 0] [0] mark(incr(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(incr(mark(X))) [0 0 0] [1] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] mark(s(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(s(mark(X))) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] mark(take(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(take(mark(X1),mark(X2))) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1] [1] mark(nil()) = [0] >= [0] = active(nil()) [1] [1] [1 1 0] [1 0 0] [1] [1 1 0] [1 0 0] [1] mark(zip(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(zip(mark(X1),mark(X2))) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] mark(pair(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(pair(mark(X1),mark(X2))) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 1 0] [0] [1 1 0] [0] mark(tail(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(tail(mark(X))) [0 0 0] [1] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] mark(repItems(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = active(repItems(mark(X))) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1 1 0] [1 0 0] [1 1 0] cons(mark(X1),X2) = [0 1 0]X1 + [0 0 1]X2 >= [0 1 0]X1 + [0 0 1]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 1 0] [1 0 0] [1 1 0] cons(active(X1),X2) = [0 1 0]X1 + [0 0 1]X2 >= [0 1 0]X1 + [0 0 1]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] incr(mark(X)) = [0 0 0]X >= [0 0 0]X = incr(X) [0 0 0] [0 0 0] [1 1 1] [1 1 0] incr(active(X)) = [0 0 0]X >= [0 0 0]X = incr(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] s(mark(X)) = [0 0 0]X >= [0 0 0]X = s(X) [0 0 0] [0 0 0] [1 0 1] [1 0 0] s(active(X)) = [0 0 0]X >= [0 0 0]X = s(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] take(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = take(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] take(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = take(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 0 0] [1 0 0] [1 0 0] take(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = take(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 1] [1 0 0] [1 0 0] take(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = take(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 0 0] [1] [1 1 0] [1 0 0] [1] zip(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = zip(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [1 0 0] [1] [1 1 0] [1 0 0] [1] zip(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = zip(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 1] [1 0 0] [1] [1 1 0] [1 0 0] [1] zip(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = zip(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [1 0 1] [1] [1 1 0] [1 0 0] [1] zip(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = zip(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] pair(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = pair(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] pair(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = pair(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 0 0] [1 0 0] [1 0 0] pair(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = pair(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 1] [1 0 0] [1 0 0] pair(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = pair(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] tail(mark(X)) = [0 0 0]X >= [0 0 0]X = tail(X) [0 0 0] [0 0 0] [1 1 1] [1 1 0] tail(active(X)) = [0 0 0]X >= [0 0 0]X = tail(X) [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] [0] repItems(mark(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = repItems(X) [0 0 0] [0] [0 0 0] [0] [1 0 1] [0] [1 0 0] [0] repItems(active(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = repItems(X) [0 0 0] [0] [0 0 0] [0] problem: active(oddNs()) -> mark(incr(pairNs())) active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) mark(pairNs()) -> active(pairNs()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(s(X)) -> active(s(mark(X))) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(zip(X1,X2)) -> active(zip(mark(X1),mark(X2))) mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2))) mark(tail(X)) -> active(tail(mark(X))) mark(repItems(X)) -> active(repItems(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) zip(mark(X1),X2) -> zip(X1,X2) zip(X1,mark(X2)) -> zip(X1,X2) zip(active(X1),X2) -> zip(X1,X2) zip(X1,active(X2)) -> zip(X1,X2) pair(mark(X1),X2) -> pair(X1,X2) pair(X1,mark(X2)) -> pair(X1,X2) pair(active(X1),X2) -> pair(X1,X2) pair(X1,active(X2)) -> pair(X1,X2) tail(mark(X)) -> tail(X) tail(active(X)) -> tail(X) repItems(mark(X)) -> repItems(X) repItems(active(X)) -> repItems(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [0] [incr](x0) = [0 0 0]x0 + [1] [0 0 1] [0], [1 0 0] [1 0 0] [1] [take](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [0], [active](x0) = x0 , [1] [oddNs] = [1] [0], [1 1 0] [1 0 0] [0] [cons](x0, x1) = [0 0 1]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 1] [1], [1 0 1] [1 0 0] [0] [zip](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 0 1] [0 0 0] [0], [0] [pairNs] = [0] [0], [1 0 0] [0] [s](x0) = [0 1 0]x0 + [0] [0 0 0] [1], [1 0 0] [1] [tail](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [1 1 0] [1] [pair](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [0], [0] [nil] = [0] [1], [1 0 0] [1] [repItems](x0) = [0 0 1]x0 + [0] [0 0 0] [0], [mark](x0) = x0 , [0] [0] = [0] [0] orientation: [1] [0] active(oddNs()) = [1] >= [1] = mark(incr(pairNs())) [0] [0] [1 1 0] [1 0 1] [1] [1 1 0] [1 0 1] [0] active(incr(cons(X,XS))) = [0 0 0]X + [0 0 0]XS + [1] >= [0 0 0]X + [0 0 0]XS + [1] = mark(cons(s(X),incr(XS))) [0 0 0] [0 0 1] [1] [0 0 0] [0 0 1] [1] [1 1 0] [1 0 1] [1 1 0] [1 0 0] [1] [1 0 0] [1 0 1] [1 1 0] [1 0 0] [1] active(zip(cons(X,XS),cons(Y,YS))) = [0 0 0]X + [0 0 0]XS + [0 0 0]Y + [0 0 0]YS + [1] >= [0 0 0]X + [0 0 0]XS + [0 0 0]Y + [0 0 0]YS + [0] = mark(cons(pair(X,Y),zip(XS,YS))) [0 0 0] [0 0 1] [0 0 0] [0 0 0] [1] [0 0 0] [0 0 1] [0 0 0] [0 0 0] [1] [0] [0] mark(pairNs()) = [0] >= [0] = active(pairNs()) [0] [0] [1 1 0] [1 0 0] [0] [1 1 0] [1 0 0] [0] mark(cons(X1,X2)) = [0 0 1]X1 + [0 0 0]X2 + [0] >= [0 0 1]X1 + [0 0 0]X2 + [0] = active(cons(mark(X1),X2)) [0 0 0] [0 0 1] [1] [0 0 0] [0 0 1] [1] [0] [0] mark(0()) = [0] >= [0] = active(0()) [0] [0] [1 0 1] [0] [1 0 1] [0] mark(incr(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = active(incr(mark(X))) [0 0 1] [0] [0 0 1] [0] [1 0 0] [0] [1 0 0] [0] mark(s(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = active(s(mark(X))) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] mark(take(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(take(mark(X1),mark(X2))) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [0] [0] mark(nil()) = [0] >= [0] = active(nil()) [1] [1] [1 0 1] [1 0 0] [0] [1 0 1] [1 0 0] [0] mark(zip(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = active(zip(mark(X1),mark(X2))) [0 0 1] [0 0 0] [0] [0 0 1] [0 0 0] [0] [1 0 0] [1 1 0] [1] [1 0 0] [1 1 0] [1] mark(pair(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(pair(mark(X1),mark(X2))) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] mark(tail(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(tail(mark(X))) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] mark(repItems(X)) = [0 0 1]X + [0] >= [0 0 1]X + [0] = active(repItems(mark(X))) [0 0 0] [0] [0 0 0] [0] [1 1 0] [1 0 0] [0] [1 1 0] [1 0 0] [0] cons(mark(X1),X2) = [0 0 1]X1 + [0 0 0]X2 + [0] >= [0 0 1]X1 + [0 0 0]X2 + [0] = cons(X1,X2) [0 0 0] [0 0 1] [1] [0 0 0] [0 0 1] [1] [1 1 0] [1 0 0] [0] [1 1 0] [1 0 0] [0] cons(active(X1),X2) = [0 0 1]X1 + [0 0 0]X2 + [0] >= [0 0 1]X1 + [0 0 0]X2 + [0] = cons(X1,X2) [0 0 0] [0 0 1] [1] [0 0 0] [0 0 1] [1] [1 0 1] [0] [1 0 1] [0] incr(mark(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = incr(X) [0 0 1] [0] [0 0 1] [0] [1 0 1] [0] [1 0 1] [0] incr(active(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = incr(X) [0 0 1] [0] [0 0 1] [0] [1 0 0] [0] [1 0 0] [0] s(mark(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = s(X) [0 0 0] [1] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] s(active(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = s(X) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] take(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = take(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] take(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = take(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] take(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = take(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] take(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = take(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 1] [1 0 0] [0] [1 0 1] [1 0 0] [0] zip(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = zip(X1,X2) [0 0 1] [0 0 0] [0] [0 0 1] [0 0 0] [0] [1 0 1] [1 0 0] [0] [1 0 1] [1 0 0] [0] zip(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = zip(X1,X2) [0 0 1] [0 0 0] [0] [0 0 1] [0 0 0] [0] [1 0 1] [1 0 0] [0] [1 0 1] [1 0 0] [0] zip(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = zip(X1,X2) [0 0 1] [0 0 0] [0] [0 0 1] [0 0 0] [0] [1 0 1] [1 0 0] [0] [1 0 1] [1 0 0] [0] zip(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = zip(X1,X2) [0 0 1] [0 0 0] [0] [0 0 1] [0 0 0] [0] [1 0 0] [1 1 0] [1] [1 0 0] [1 1 0] [1] pair(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = pair(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 1 0] [1] [1 0 0] [1 1 0] [1] pair(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = pair(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 1 0] [1] [1 0 0] [1 1 0] [1] pair(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = pair(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 1 0] [1] [1 0 0] [1 1 0] [1] pair(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = pair(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] tail(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = tail(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] tail(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = tail(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] repItems(mark(X)) = [0 0 1]X + [0] >= [0 0 1]X + [0] = repItems(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] repItems(active(X)) = [0 0 1]X + [0] >= [0 0 1]X + [0] = repItems(X) [0 0 0] [0] [0 0 0] [0] problem: active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) mark(pairNs()) -> active(pairNs()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(s(X)) -> active(s(mark(X))) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(zip(X1,X2)) -> active(zip(mark(X1),mark(X2))) mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2))) mark(tail(X)) -> active(tail(mark(X))) mark(repItems(X)) -> active(repItems(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) zip(mark(X1),X2) -> zip(X1,X2) zip(X1,mark(X2)) -> zip(X1,X2) zip(active(X1),X2) -> zip(X1,X2) zip(X1,active(X2)) -> zip(X1,X2) pair(mark(X1),X2) -> pair(X1,X2) pair(X1,mark(X2)) -> pair(X1,X2) pair(active(X1),X2) -> pair(X1,X2) pair(X1,active(X2)) -> pair(X1,X2) tail(mark(X)) -> tail(X) tail(active(X)) -> tail(X) repItems(mark(X)) -> repItems(X) repItems(active(X)) -> repItems(X) Matrix Interpretation Processor: dim=1 interpretation: [incr](x0) = x0, [take](x0, x1) = x0 + x1, [active](x0) = x0, [cons](x0, x1) = x0 + x1 + 1, [zip](x0, x1) = x0 + 2x1, [pairNs] = 6, [s](x0) = 2x0 + 4, [tail](x0) = 2x0, [pair](x0, x1) = x0 + 2x1 + 1, [nil] = 4, [repItems](x0) = 4x0 + 6, [mark](x0) = x0, [0] = 4 orientation: active(zip(cons(X,XS),cons(Y,YS))) = X + XS + 2Y + 2YS + 3 >= X + XS + 2Y + 2YS + 2 = mark(cons(pair(X,Y),zip(XS,YS))) mark(pairNs()) = 6 >= 6 = active(pairNs()) mark(cons(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = active(cons(mark(X1),X2)) mark(0()) = 4 >= 4 = active(0()) mark(incr(X)) = X >= X = active(incr(mark(X))) mark(s(X)) = 2X + 4 >= 2X + 4 = active(s(mark(X))) mark(take(X1,X2)) = X1 + X2 >= X1 + X2 = active(take(mark(X1),mark(X2))) mark(nil()) = 4 >= 4 = active(nil()) mark(zip(X1,X2)) = X1 + 2X2 >= X1 + 2X2 = active(zip(mark(X1),mark(X2))) mark(pair(X1,X2)) = X1 + 2X2 + 1 >= X1 + 2X2 + 1 = active(pair(mark(X1),mark(X2))) mark(tail(X)) = 2X >= 2X = active(tail(mark(X))) mark(repItems(X)) = 4X + 6 >= 4X + 6 = active(repItems(mark(X))) cons(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = cons(X1,X2) cons(active(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = cons(X1,X2) incr(mark(X)) = X >= X = incr(X) incr(active(X)) = X >= X = incr(X) s(mark(X)) = 2X + 4 >= 2X + 4 = s(X) s(active(X)) = 2X + 4 >= 2X + 4 = s(X) take(mark(X1),X2) = X1 + X2 >= X1 + X2 = take(X1,X2) take(X1,mark(X2)) = X1 + X2 >= X1 + X2 = take(X1,X2) take(active(X1),X2) = X1 + X2 >= X1 + X2 = take(X1,X2) take(X1,active(X2)) = X1 + X2 >= X1 + X2 = take(X1,X2) zip(mark(X1),X2) = X1 + 2X2 >= X1 + 2X2 = zip(X1,X2) zip(X1,mark(X2)) = X1 + 2X2 >= X1 + 2X2 = zip(X1,X2) zip(active(X1),X2) = X1 + 2X2 >= X1 + 2X2 = zip(X1,X2) zip(X1,active(X2)) = X1 + 2X2 >= X1 + 2X2 = zip(X1,X2) pair(mark(X1),X2) = X1 + 2X2 + 1 >= X1 + 2X2 + 1 = pair(X1,X2) pair(X1,mark(X2)) = X1 + 2X2 + 1 >= X1 + 2X2 + 1 = pair(X1,X2) pair(active(X1),X2) = X1 + 2X2 + 1 >= X1 + 2X2 + 1 = pair(X1,X2) pair(X1,active(X2)) = X1 + 2X2 + 1 >= X1 + 2X2 + 1 = pair(X1,X2) tail(mark(X)) = 2X >= 2X = tail(X) tail(active(X)) = 2X >= 2X = tail(X) repItems(mark(X)) = 4X + 6 >= 4X + 6 = repItems(X) repItems(active(X)) = 4X + 6 >= 4X + 6 = repItems(X) problem: mark(pairNs()) -> active(pairNs()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(s(X)) -> active(s(mark(X))) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(zip(X1,X2)) -> active(zip(mark(X1),mark(X2))) mark(pair(X1,X2)) -> active(pair(mark(X1),mark(X2))) mark(tail(X)) -> active(tail(mark(X))) mark(repItems(X)) -> active(repItems(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) zip(mark(X1),X2) -> zip(X1,X2) zip(X1,mark(X2)) -> zip(X1,X2) zip(active(X1),X2) -> zip(X1,X2) zip(X1,active(X2)) -> zip(X1,X2) pair(mark(X1),X2) -> pair(X1,X2) pair(X1,mark(X2)) -> pair(X1,X2) pair(active(X1),X2) -> pair(X1,X2) pair(X1,active(X2)) -> pair(X1,X2) tail(mark(X)) -> tail(X) tail(active(X)) -> tail(X) repItems(mark(X)) -> repItems(X) repItems(active(X)) -> repItems(X) Matrix Interpretation Processor: dim=1 interpretation: [incr](x0) = 2x0, [take](x0, x1) = 4x0 + 4x1 + 2, [active](x0) = x0, [cons](x0, x1) = 2x0 + 2x1 + 6, [zip](x0, x1) = 2x0 + 4x1 + 3, [pairNs] = 2, [s](x0) = 4x0 + 6, [tail](x0) = 4x0 + 4, [pair](x0, x1) = 2x0 + 4x1 + 2, [nil] = 1, [repItems](x0) = x0, [mark](x0) = 4x0, [0] = 0 orientation: mark(pairNs()) = 8 >= 2 = active(pairNs()) mark(cons(X1,X2)) = 8X1 + 8X2 + 24 >= 8X1 + 2X2 + 6 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(incr(X)) = 8X >= 8X = active(incr(mark(X))) mark(s(X)) = 16X + 24 >= 16X + 6 = active(s(mark(X))) mark(take(X1,X2)) = 16X1 + 16X2 + 8 >= 16X1 + 16X2 + 2 = active(take(mark(X1),mark(X2))) mark(nil()) = 4 >= 1 = active(nil()) mark(zip(X1,X2)) = 8X1 + 16X2 + 12 >= 8X1 + 16X2 + 3 = active(zip(mark(X1),mark(X2))) mark(pair(X1,X2)) = 8X1 + 16X2 + 8 >= 8X1 + 16X2 + 2 = active(pair(mark(X1),mark(X2))) mark(tail(X)) = 16X + 16 >= 16X + 4 = active(tail(mark(X))) mark(repItems(X)) = 4X >= 4X = active(repItems(mark(X))) cons(mark(X1),X2) = 8X1 + 2X2 + 6 >= 2X1 + 2X2 + 6 = cons(X1,X2) cons(active(X1),X2) = 2X1 + 2X2 + 6 >= 2X1 + 2X2 + 6 = cons(X1,X2) incr(mark(X)) = 8X >= 2X = incr(X) incr(active(X)) = 2X >= 2X = incr(X) s(mark(X)) = 16X + 6 >= 4X + 6 = s(X) s(active(X)) = 4X + 6 >= 4X + 6 = s(X) take(mark(X1),X2) = 16X1 + 4X2 + 2 >= 4X1 + 4X2 + 2 = take(X1,X2) take(X1,mark(X2)) = 4X1 + 16X2 + 2 >= 4X1 + 4X2 + 2 = take(X1,X2) take(active(X1),X2) = 4X1 + 4X2 + 2 >= 4X1 + 4X2 + 2 = take(X1,X2) take(X1,active(X2)) = 4X1 + 4X2 + 2 >= 4X1 + 4X2 + 2 = take(X1,X2) zip(mark(X1),X2) = 8X1 + 4X2 + 3 >= 2X1 + 4X2 + 3 = zip(X1,X2) zip(X1,mark(X2)) = 2X1 + 16X2 + 3 >= 2X1 + 4X2 + 3 = zip(X1,X2) zip(active(X1),X2) = 2X1 + 4X2 + 3 >= 2X1 + 4X2 + 3 = zip(X1,X2) zip(X1,active(X2)) = 2X1 + 4X2 + 3 >= 2X1 + 4X2 + 3 = zip(X1,X2) pair(mark(X1),X2) = 8X1 + 4X2 + 2 >= 2X1 + 4X2 + 2 = pair(X1,X2) pair(X1,mark(X2)) = 2X1 + 16X2 + 2 >= 2X1 + 4X2 + 2 = pair(X1,X2) pair(active(X1),X2) = 2X1 + 4X2 + 2 >= 2X1 + 4X2 + 2 = pair(X1,X2) pair(X1,active(X2)) = 2X1 + 4X2 + 2 >= 2X1 + 4X2 + 2 = pair(X1,X2) tail(mark(X)) = 16X + 4 >= 4X + 4 = tail(X) tail(active(X)) = 4X + 4 >= 4X + 4 = tail(X) repItems(mark(X)) = 4X >= X = repItems(X) repItems(active(X)) = X >= X = repItems(X) problem: mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(repItems(X)) -> active(repItems(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) incr(mark(X)) -> incr(X) incr(active(X)) -> incr(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) zip(mark(X1),X2) -> zip(X1,X2) zip(X1,mark(X2)) -> zip(X1,X2) zip(active(X1),X2) -> zip(X1,X2) zip(X1,active(X2)) -> zip(X1,X2) pair(mark(X1),X2) -> pair(X1,X2) pair(X1,mark(X2)) -> pair(X1,X2) pair(active(X1),X2) -> pair(X1,X2) pair(X1,active(X2)) -> pair(X1,X2) tail(mark(X)) -> tail(X) tail(active(X)) -> tail(X) repItems(mark(X)) -> repItems(X) repItems(active(X)) -> repItems(X) Matrix Interpretation Processor: dim=1 interpretation: [incr](x0) = x0 + 2, [take](x0, x1) = 4x0 + 4x1 + 6, [active](x0) = x0 + 2, [cons](x0, x1) = x0 + x1, [zip](x0, x1) = x0 + 4x1 + 5, [s](x0) = 4x0, [tail](x0) = 2x0 + 6, [pair](x0, x1) = 4x0 + 3x1 + 3, [repItems](x0) = 4x0 + 2, [mark](x0) = 2x0, [0] = 2 orientation: mark(0()) = 4 >= 4 = active(0()) mark(incr(X)) = 2X + 4 >= 2X + 4 = active(incr(mark(X))) mark(repItems(X)) = 8X + 4 >= 8X + 4 = active(repItems(mark(X))) cons(mark(X1),X2) = 2X1 + X2 >= X1 + X2 = cons(X1,X2) cons(active(X1),X2) = X1 + X2 + 2 >= X1 + X2 = cons(X1,X2) incr(mark(X)) = 2X + 2 >= X + 2 = incr(X) incr(active(X)) = X + 4 >= X + 2 = incr(X) s(mark(X)) = 8X >= 4X = s(X) s(active(X)) = 4X + 8 >= 4X = s(X) take(mark(X1),X2) = 8X1 + 4X2 + 6 >= 4X1 + 4X2 + 6 = take(X1,X2) take(X1,mark(X2)) = 4X1 + 8X2 + 6 >= 4X1 + 4X2 + 6 = take(X1,X2) take(active(X1),X2) = 4X1 + 4X2 + 14 >= 4X1 + 4X2 + 6 = take(X1,X2) take(X1,active(X2)) = 4X1 + 4X2 + 14 >= 4X1 + 4X2 + 6 = take(X1,X2) zip(mark(X1),X2) = 2X1 + 4X2 + 5 >= X1 + 4X2 + 5 = zip(X1,X2) zip(X1,mark(X2)) = X1 + 8X2 + 5 >= X1 + 4X2 + 5 = zip(X1,X2) zip(active(X1),X2) = X1 + 4X2 + 7 >= X1 + 4X2 + 5 = zip(X1,X2) zip(X1,active(X2)) = X1 + 4X2 + 13 >= X1 + 4X2 + 5 = zip(X1,X2) pair(mark(X1),X2) = 8X1 + 3X2 + 3 >= 4X1 + 3X2 + 3 = pair(X1,X2) pair(X1,mark(X2)) = 4X1 + 6X2 + 3 >= 4X1 + 3X2 + 3 = pair(X1,X2) pair(active(X1),X2) = 4X1 + 3X2 + 11 >= 4X1 + 3X2 + 3 = pair(X1,X2) pair(X1,active(X2)) = 4X1 + 3X2 + 9 >= 4X1 + 3X2 + 3 = pair(X1,X2) tail(mark(X)) = 4X + 6 >= 2X + 6 = tail(X) tail(active(X)) = 2X + 10 >= 2X + 6 = tail(X) repItems(mark(X)) = 8X + 2 >= 4X + 2 = repItems(X) repItems(active(X)) = 4X + 10 >= 4X + 2 = repItems(X) problem: mark(0()) -> active(0()) mark(incr(X)) -> active(incr(mark(X))) mark(repItems(X)) -> active(repItems(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) incr(mark(X)) -> incr(X) s(mark(X)) -> s(X) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) zip(mark(X1),X2) -> zip(X1,X2) zip(X1,mark(X2)) -> zip(X1,X2) pair(mark(X1),X2) -> pair(X1,X2) pair(X1,mark(X2)) -> pair(X1,X2) tail(mark(X)) -> tail(X) repItems(mark(X)) -> repItems(X) Matrix Interpretation Processor: dim=1 interpretation: [incr](x0) = 4x0 + 2, [take](x0, x1) = x0 + x1 + 3, [active](x0) = x0, [cons](x0, x1) = 4x0 + x1, [zip](x0, x1) = x0 + 4x1 + 1, [s](x0) = 2x0, [tail](x0) = 4x0, [pair](x0, x1) = x0 + 4x1, [repItems](x0) = x0 + 1, [mark](x0) = 4x0, [0] = 0 orientation: mark(0()) = 0 >= 0 = active(0()) mark(incr(X)) = 16X + 8 >= 16X + 2 = active(incr(mark(X))) mark(repItems(X)) = 4X + 4 >= 4X + 1 = active(repItems(mark(X))) cons(mark(X1),X2) = 16X1 + X2 >= 4X1 + X2 = cons(X1,X2) incr(mark(X)) = 16X + 2 >= 4X + 2 = incr(X) s(mark(X)) = 8X >= 2X = s(X) take(mark(X1),X2) = 4X1 + X2 + 3 >= X1 + X2 + 3 = take(X1,X2) take(X1,mark(X2)) = X1 + 4X2 + 3 >= X1 + X2 + 3 = take(X1,X2) zip(mark(X1),X2) = 4X1 + 4X2 + 1 >= X1 + 4X2 + 1 = zip(X1,X2) zip(X1,mark(X2)) = X1 + 16X2 + 1 >= X1 + 4X2 + 1 = zip(X1,X2) pair(mark(X1),X2) = 4X1 + 4X2 >= X1 + 4X2 = pair(X1,X2) pair(X1,mark(X2)) = X1 + 16X2 >= X1 + 4X2 = pair(X1,X2) tail(mark(X)) = 16X >= 4X = tail(X) repItems(mark(X)) = 4X + 1 >= X + 1 = repItems(X) problem: mark(0()) -> active(0()) cons(mark(X1),X2) -> cons(X1,X2) incr(mark(X)) -> incr(X) s(mark(X)) -> s(X) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) zip(mark(X1),X2) -> zip(X1,X2) zip(X1,mark(X2)) -> zip(X1,X2) pair(mark(X1),X2) -> pair(X1,X2) pair(X1,mark(X2)) -> pair(X1,X2) tail(mark(X)) -> tail(X) repItems(mark(X)) -> repItems(X) Matrix Interpretation Processor: dim=1 interpretation: [incr](x0) = x0 + 2, [take](x0, x1) = x0 + 2x1 + 1, [active](x0) = x0 + 7, [cons](x0, x1) = 4x0 + 4x1, [zip](x0, x1) = 4x0 + 4x1, [s](x0) = 3x0, [tail](x0) = 3x0 + 2, [pair](x0, x1) = x0 + 4x1, [repItems](x0) = x0, [mark](x0) = 4x0, [0] = 3 orientation: mark(0()) = 12 >= 10 = active(0()) cons(mark(X1),X2) = 16X1 + 4X2 >= 4X1 + 4X2 = cons(X1,X2) incr(mark(X)) = 4X + 2 >= X + 2 = incr(X) s(mark(X)) = 12X >= 3X = s(X) take(mark(X1),X2) = 4X1 + 2X2 + 1 >= X1 + 2X2 + 1 = take(X1,X2) take(X1,mark(X2)) = X1 + 8X2 + 1 >= X1 + 2X2 + 1 = take(X1,X2) zip(mark(X1),X2) = 16X1 + 4X2 >= 4X1 + 4X2 = zip(X1,X2) zip(X1,mark(X2)) = 4X1 + 16X2 >= 4X1 + 4X2 = zip(X1,X2) pair(mark(X1),X2) = 4X1 + 4X2 >= X1 + 4X2 = pair(X1,X2) pair(X1,mark(X2)) = X1 + 16X2 >= X1 + 4X2 = pair(X1,X2) tail(mark(X)) = 12X + 2 >= 3X + 2 = tail(X) repItems(mark(X)) = 4X >= X = repItems(X) problem: cons(mark(X1),X2) -> cons(X1,X2) incr(mark(X)) -> incr(X) s(mark(X)) -> s(X) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) zip(mark(X1),X2) -> zip(X1,X2) zip(X1,mark(X2)) -> zip(X1,X2) pair(mark(X1),X2) -> pair(X1,X2) pair(X1,mark(X2)) -> pair(X1,X2) tail(mark(X)) -> tail(X) repItems(mark(X)) -> repItems(X) Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [incr](x0) = [0 0 0]x0 [0 0 1] , [1 0 0] [1 1 0] [take](x0, x1) = [0 0 0]x0 + [0 1 0]x1 [1 0 0] [1 0 0] , [1 0 0] [1 0 0] [1] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 1 0] [0 0 0] [0], [1 0 0] [1 0 0] [zip](x0, x1) = [0 0 1]x0 + [0 0 0]x1 [0 0 0] [1 0 0] , [1 0 0] [1] [s](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [tail](x0) = [0 0 1]x0 [0 0 1] , [1 0 0] [1 1 0] [pair](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 1 0] [repItems](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [mark](x0) = [0 1 1]x0 + [1] [1 0 1] [0] orientation: [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] cons(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = cons(X1,X2) [0 1 1] [0 0 0] [1] [0 1 0] [0 0 0] [0] [1 1 1] [1] [1 1 0] incr(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X = incr(X) [1 0 1] [0] [0 0 1] [1 0 0] [1] [1 0 0] [1] s(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = s(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 1 0] [1 0 0] [1 1 0] take(mark(X1),X2) = [0 0 0]X1 + [0 1 0]X2 >= [0 0 0]X1 + [0 1 0]X2 = take(X1,X2) [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 1 1] [1] [1 0 0] [1 1 0] take(X1,mark(X2)) = [0 0 0]X1 + [0 1 1]X2 + [1] >= [0 0 0]X1 + [0 1 0]X2 = take(X1,X2) [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] zip(mark(X1),X2) = [1 0 1]X1 + [0 0 0]X2 >= [0 0 1]X1 + [0 0 0]X2 = zip(X1,X2) [0 0 0] [1 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] zip(X1,mark(X2)) = [0 0 1]X1 + [0 0 0]X2 >= [0 0 1]X1 + [0 0 0]X2 = zip(X1,X2) [0 0 0] [1 0 0] [0 0 0] [1 0 0] [1 0 0] [1 1 0] [1 0 0] [1 1 0] pair(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = pair(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 1 1] [1] [1 0 0] [1 1 0] pair(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = pair(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] tail(mark(X)) = [1 0 1]X >= [0 0 1]X = tail(X) [1 0 1] [0 0 1] [1 1 1] [1] [1 1 0] repItems(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X = repItems(X) [0 0 0] [0] [0 0 0] problem: cons(mark(X1),X2) -> cons(X1,X2) s(mark(X)) -> s(X) take(mark(X1),X2) -> take(X1,X2) zip(mark(X1),X2) -> zip(X1,X2) zip(X1,mark(X2)) -> zip(X1,X2) pair(mark(X1),X2) -> pair(X1,X2) tail(mark(X)) -> tail(X) Matrix Interpretation Processor: dim=1 interpretation: [take](x0, x1) = 2x0 + 2x1, [cons](x0, x1) = x0 + 2x1, [zip](x0, x1) = 2x0 + 2x1 + 2, [s](x0) = x0 + 2, [tail](x0) = 4x0, [pair](x0, x1) = 2x0 + x1 + 2, [mark](x0) = 4x0 + 7 orientation: cons(mark(X1),X2) = 4X1 + 2X2 + 7 >= X1 + 2X2 = cons(X1,X2) s(mark(X)) = 4X + 9 >= X + 2 = s(X) take(mark(X1),X2) = 8X1 + 2X2 + 14 >= 2X1 + 2X2 = take(X1,X2) zip(mark(X1),X2) = 8X1 + 2X2 + 16 >= 2X1 + 2X2 + 2 = zip(X1,X2) zip(X1,mark(X2)) = 2X1 + 8X2 + 16 >= 2X1 + 2X2 + 2 = zip(X1,X2) pair(mark(X1),X2) = 8X1 + X2 + 16 >= 2X1 + X2 + 2 = pair(X1,X2) tail(mark(X)) = 16X + 28 >= 4X = tail(X) problem: Qed